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Book SynopsisFrom H.G. Wells to Star Trek, audiences have been captivated by the notions of time travel, time warps, space warps, and wornholes. But science fiction is not the only realm where these concepts thrive. An active group of general relativists and quantum field theorists has produced a considerable body of serious (thought admittedly speculative) mathematical and physical analyses of the wormhole system. Now, with this fascinating book, readers can explore in depth the science behind the science fiction. Drawing on pivotal work by Einstein, Wheeler, Morris, Thorne, Hawking, and others, Matt Visser charts the development and current state of Lorentzian wormhole physics. Dr. Visser shows that by pushing established physical theories to their limits, it is possible to deduce the physical properties of such exotica as wormholes and time travel. The physical framework he uses is derived from one of the major research frontiers of modern theoretical physics: quantum gravity-the intersection of classical Einstein gravity and quantum field theory. Physicists, students of general relativity, cosmology, quantum physics, or any interested reader with a background in physics wil find this a provocative introduction to an exciting and active topic of ongoing research.Table of ContentsPreface; Acknowledgments; I. Background: 1. Introduction; 2. General Relativity; 3. Quantum Field Theory; 4. Units and Natural Scales; II. History: 5. The Einstein-Rosen Bridge; 6. Spacetime Foam; 7. The Kerr Wormhole; 8. The Cosmological Constant; 9. Wormhole Taxonomy; 10. Interregnum; III. Renaissance: 11. Traversible Wormholes; 12. Energy Conditions; 13. Engineering Considerations; 14. Thin Shells: Fromalism; 15. Thin Shells: Wormholes; 16. Topological Censorship; IV.: Time Travel: 17. Chronology: Basic Notions; 18. From Wormhole to Time Machine; 19. Response to the Paradoxes; V. Quantum Effects; 20. Semiclassical Quantum Gravity; 21. van Vleck Determinants: Formalism; 22. van Vleck Determinants: Wormholes; 23. Singularity Structure; 24. Minisuperspace Wormholes; VI. Reprise: 25. Where We Stand; Bibliography; Index

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Book SynopsisBased on a course taught for years at Oxford, this book offers a concise exposition of the central ideas of general relativity. The focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. Includes links to recent developments, including theoretical work and observational evidence, to encourage further study.Trade ReviewFrom the reviews:“This book introduces General Relativity at students level, especially intended for final year mathematics students. Different from other books with the same title, it really goes into the geometric details and tries to explain the given formulae … . The appendices present exercises and hints to their solutions.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, May, 2014)"I have the opportunity to comment on General Relativity … . I am happy to recommend … for an advanced undergraduate course on relativity or for self-study. … marvelous faithfulness to historical developments … characterizes the entire treatment. … In fact, the whole book is distinguished by this high quality of exposition. … It’s a fine book, beautifully written and clear, and I highly recommend it." (Michael Berg, MathDL, January, 2007)MAA Reviews:In December, 2003 I had the pleasure of reviewing the admirable book Special Relativity, by N.M.J. Woodhouse, and now I have the opportunity to comment on General Relativity by the same author. I am happy to recommend not just this sequel, but the indicated pair, for an advanced undergraduate course on relativity or for self-study.One particularly noteworthy feature of General Relativity is that woodhouse seeks to present the subject neither as a branch of differential geometry nor as the kind of physics mathematicians like me find unapproachable (and I'm afraid this doesn't particularly narrow the field). When just a rookie I dabbled in relativity largely from popularizations and biographical writings, and when I tried to learn some real general relativity in graduate school - for cultural reasons, I guess - it simply didn't take. But my interest in the subject, both specially and generally, has never flagged and Woodhouse’s books are tailor-made for even my lingering ambitions. In other words, for any slacker who feels he should have learned this beautiful material in his mathematical youth, but didn’t, and is now secretly (or not so secretly) desirous of doing it right, this is the book, or, more correctly, these are the books to read. Furthermore, as I already hinted, as far as teaching courses on these important subjects is concerned, obviously these books fit that bill very well too, given Woodhouse’s specific pedagogical intent.When it comes to the specific style and presentation of general relativity chosen by Woodhouse, marvellous faithfulness to historical developments, in particular Einstein’s own writings, characterizes the entire treatment. On p.7, already, the weak and strong equivalence principles are presented and analysed in a succinct and historically rooted fashion. The former, going back to Galileo’s pendulums (Woodhouse correctly says "pendula," of course) and famously connected with Eötvös’ experiment, entails that inertial mass and gravitational mass are the same; and the latter says that there are no obvservable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these observable differences between the local effects of gravity and acceleration. Woodhouse’s brief discussion of these incomparable axioms underlying Einstein’s revolution is a gem of exposition, covering the historical sweep of the attendant experiments (he even mentions a planned space experiment, "STEP," which will test the latter principle to within one part in 1018) and conveying what is to come as a result of these stipulations. Finally, I want to draw special attention to pp.23-27, where Woodhouse does a phenomenally good job of explicating the subject of tensors in Minkowski space, a subject which has always been a bit unsettling to me who was raised to visit tensor products in their homological algebraic home and I cannot resist mentioning Problem 1.5 on p.13, dealing with "Einstein’s birthday present."It’s a fine book, beautifully written and clear, and I highly recommend it. [Reviewed by Michael Berg, 20.1.2007]"Woodhouse … lets the physical intuition behind relativity inform every step of its logical development, making his treatment as digestible as any in print. He does introduce ab ovo what differential geometry he needs, and he takes the whole theory far enough to develop general relativity’s most exciting predictions, black holes and gravity waves, all in less than half the number of pages one might expect. Summing Up: Highly recommended. Upper-division undergraduates through professionals." (D. V. Feldman, CHOICE, Vol. 44 (11), July, 2007)"The book is an outgrowth of a lecture course given over many years by the author and his colleagues to final-year applied mathematicians at the Mathematical Institute in Oxford, UK. The book is well-written and easy to follow because the author constructs the necessary apparatus layer-by-layer, from the bottom up, carefully motivating and justifying every new concept. Exercises are given at the end of every chapter … and numerous examples appear throughout the text. … its expository style is very appealing." (David A. Burton, General Relativity and Gravitation, Vol. 39, 2007)Table of ContentsNewtonian Gravity.- Inertial Coordinates and Tensors.- Energy-Momentum Tensors.- Curved Space—Time.- Tensor Calculus.- Einstein’s Equation.- Spherical Symmetry.- Orbits in the Schwarzschild Space—Time.- Black Holes.- Rotating Bodies.- Gravitational Waves.- Redshift and Horizons.

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Book SynopsisThis book provides readers with the tools needed to understand the physical basis of special relativity and will enable a confident mathematical understanding of Minkowski's picture of space-time. It features a large number of examples and exercises, ranging from the rather simple through to the more involved and challenging. Coverage includes acceleration and tensors and has an emphasis on space-time diagrams.Trade ReviewFrom the reviews: N.M.J. Woodhouse's comparatively short Special Relativity is a pleasure to read and therefore qualifies right off as a good source to use for learning about special relativity on your own. A lot of very nice material is touched on in its pages, presented in natural sequence consonant with history, and is not improperly belabored. It's also rather informal in style. One gets the sense of breezing along pretty fast while, in actuality, a lot of material is being dealt with... the selection of topics in the book is very nice indeed , and is historically sound and will therefore reward the reader with an element of culture to boot: he'll learn some history of modern physics... I wish this book had been around when I was a student. MAA Online ...an exciting and challenging book with which to introduce a modern mathematics student in a single course to the great ideas of Maxwell's theory and special relativity. The Australian Mathematical Society Gazette "There are many books on special relativity for undergraduates, and this one is notable in that it is specifically addressed to mathematicians. … this book will be found illuminating by students of mathematics … ." (Dr. P. E. Hodgson, Contemporary Physics, Vol. 45 (5), 2004) "This book is … aimed squarely at the undergraduate mathematician ... . The tone, pace and level of the book are nicely judged for middle level undergraduates studying mathematics. … There are lots of examples and nicely graded exercises throughout the text, and each chapter ends with a usefully annotated bibliography. The author’s friendly style, and the fact the material has been developed from taught courses make the book ideal for self-study … ." (Peter Macgregor, The Mathematical Gazette, Vol. 88 (512), 2004) "Meant as a resource for advanced undergraduate students, this book approaches special relativity theory from a mathematical perspective … . It is best used for mathematics majors … . the text is clear, well written, and has an adequate bibliography. Summing Up: Recommended. Upper-division undergraduates." (A. Spero, CHOICE, December, 2003) "This presentation is very elegant … . The book contains a large number of examples. Each chapter is followed by exercises, ranging from the rather simple to the more involved. This book is certainly a good introduction to special relativity, understandable for second-year students. But it is also interesting for readers searching for a concise and precise presentation of special relativity within the tensor formalism." (Claude Semay, Physcalia, Vol. 25 (4), 2003)Table of Contents1. Relativity in Classical Mechanics.- 1.1 Frames of Reference.- 1.2 Relativity.- 1.3 Frames of Reference.- 1.4 Newton’s Laws.- 1.5 Galilean Transformations.- 1.6 Mass, Energy, and Momentum.- 1.7 Space-time.- 1.8 *Galilean Symmetries.- 1.9 Historical Note.- 2. Maxwell’s Theory.- 2.1 Introduction.- 2.2 The Unification of Electricity and Magnetism.- 2.3 Charges, Fields, and the Lorentz Force Law.- 2.4 Stationary Distributions of Charge.- 2.5 The Divergence of the Magnetic Field.- 2.6 Inconsistency with Galilean Relativity.- 2.7 The Limits of Galilean Invariance.- 2.8 Faraday’s Law of Induction.- 2.9 The Field of Charges in Uniform Motion.- 2.10 Maxwell’s Equations.- 2.11 The Continuity Equation.- 2.12 Conservation of Charge.- 2.13 Historical Note.- 3. The Propagation of Light.- 3.1 The Displacement Current.- 3.2 The Source-free Equations.- 3.3 The Wave Equation.- 3.4 Monochromatic Plane Waves.- 3.5 Polarization.- 3.6 Potentials.- 3.7 Gauge Transformations.- 3.8 Photons.- 3.9 Relativity and the Propagation of Light.- 3.10 The Michelson-Morley Experiment.- 4. Einstein’s Special Theory of Relativity.- 4.1 Lorentz’s Contraction.- 4.2 Operational Definitions of Distance and Time.- 4.3 The Relativity of Simultaneity.- 4.4 Bondi’s fc-Factor.- 4.5 Time Dilation.- 4.6 The Two-dimensional Lorentz Transformation.- 4.7 Transformation of Velocity.- 4.8 The Lorentz Contraction.- 4.9 Composition of Lorentz Transformations.- 4.10 Rapidity.- 4.11 *The Lorentz and Poincaré Groups.- 5. Lorentz Transformations in Four Dimensions.- 5.1 Coordinates in Four Dimensions.- 5.2 Four-dimensional Coordinate Transformations.- 5.3 The Lorentz Transformation in Four Dimensions.- 5.4 The Standard Lorentz Transformation.- 5.5 The General Lorentz Transformation.- 5.6 Euclidean Space and Minkowski Space.- 5.7 Four-vectors.- 5.8 Temporal and Spatial Parts.- 5.9 The Inner Product.- 5.10 Classification of Four-vectors.- 5.11 Causal Structure of Minkowski Space.- 5.12 Invariant Operators.- 5.13 The Frequency Four-vector.- 5.14 * Affine Spaces and Covectors.- 6. Relative Motion.- 6.1 Transformations Between Frames.- 6.2 Proper Time.- 6.3 Four-velocity.- 6.4 Four-acceleration.- 6.5 Constant Acceleration.- 6.6 Continuous Distributions.- 6.7 *Rigid Body Motion.- 6.8 Visual Observation.- 7. Relativistic Collisions.- 7.1 The Operational Definition of Mass.- 7.2 Conservation of Four-momentum.- 7.3 Equivalence of Mass and Energy.- 8. Relativistic Electrodynamics.- 8.1 Lorentz Transformations of E and B.- 8.2 The Four-Current and the Four-potential.- 8.3 Transformations of E and B.- 8.4 Linearly Polarized Plane Waves.- 8.5 Electromagnetic Energy.- 8.6 The Four-momentum of a Photon.- 8.7 *Advanced and Retarded Solutions.- 9. *Tensors and Isomet ries.- 9.1 Affine Space.- 9.2 The Lorentz Group.- 9.3 Tensors.- 9.4 The Tensor Product.- 9.5 Tensors in Minkowski Space.- 9.6 Tensor Components.- 9.7 Examples of Tensors.- 9.8 One-parameter Subgroups.- 9.9 Isometries.- 9.10 The Riemann Sphere and Spinors.- Notes on Exercises.- Vector Calculus.

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Book SynopsisThis primer is a collection of notes based on lectures that were originally given at IIT Madras (India) and at IFT Madrid (Spain). It is a concise and pragmatic course on applied holography focusing on the basic analytic and numerical techniques involved. The presented lectures are not intended to provide all the fundamental theoretical background, which can be found in the available literature, but they concentrate on concrete applications of AdS/CFT to hydrodynamics, quantum chromodynamics and condensed matter. The idea is to accompany the reader step by step through the various benchmark examples with a classmate attitude, providing details for the computations and open-source numerical codes in Mathematica, and sharing simple tricks and warnings collected during the author’s research experience. At the end of this path, the reader will be in possess of all the fundamental skills and tools to learn by him/herself more advanced techniques and to produce independent and novel research in the field.Table of ContentsA Strings-less introduction to AdS-CFT.- A Practical Understanding of the Dictionary.- The first big success: η/s and Hydrodynamics.- Holographic Transport via analytic and numerical techniques.

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Book SynopsisThis book provides an in-depth and accessible description of special relativity and quantum mechanics which together form the foundation of 21st century physics. A novel aspect is that symmetry is given its rightful prominence as an integral part of this foundation. The book offers not only a conceptual understanding of symmetry, but also the mathematical tools necessary for quantitative analysis. As such, it provides a valuable precursor to more focused, advanced books on special relativity or quantum mechanics.Students are introduced to several topics not typically covered until much later in their education.These include space-time diagrams, the action principle, a proof of Noether's theorem, Lorentz vectors and tensors, symmetry breaking and general relativity. The book also provides extensive descriptions on topics of current general interest such as gravitational waves, cosmology, Bell's theorem, entanglement and quantum computing.Throughout the text, every opportunity is taken to emphasize the intimate connection between physics, symmetry and mathematics.The style remains light despite the rigorous and intensive content. The book is intended as a stand-alone or supplementary physics text for a one or two semester course for students who have completed an introductory calculus course and a first-year physics course that includes Newtonian mechanics and some electrostatics. Basic knowledge of linear algebra is useful but not essential, as all requisite mathematical background is provided either in the body of the text or in the Appendices. Interspersed through the text are well over a hundred worked examples and unsolved exercises for the student.Table of Contents1 Introduction 91.1 The goal of physics . . . . . . . . . . . . . . . . . . . . . . . . 91.2 The connection between physics and mathematics . . . . . . . 101.3 Paradigm shifts . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 The Correspondence Principle . . . . . . . . . . . . . . . . . . 162 Symmetry and Physics 172.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 172.2 What is Symmetry? . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Role of Symmetry in Physics . . . . . . . . . . . . . . . . . . . 182.3.1 Symmetry as a guiding principle . . . . . . . . . . . . . 182.3.2 Symmetry and Conserved Quantities: Noether's Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.3 Symmetry as a tool for simplifying problems . . . . . . 192.4 Symmetries were made to be broken . . . . . . . . . . . . . . 202.4.1 Spacetime symmetries . . . . . . . . . . . . . . . . . . 202.4.2 Parity violation . . . . . . . . . . . . . . . . . . . . . . 212.4.3 Spontaneously broken symmetries . . . . . . . . . . . . 242.4.4 Variational calculations: Lifeguards and light rays . . . 273 Formal Aspects of Symmetry 303.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Symmetries and Operations . . . . . . . . . . . . . . . . . . . 303.2.1 Denition of a symmetry operation . . . . . . . . . . . 303.2.2 Rules obeyed by symmetry operations . . . . . . . . . 323.2.3 Multiplication tables . . . . . . . . . . . . . . . . . . . 353.2.4 Symmetry and group theory . . . . . . . . . . . . . . . 363.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 The identity operation . . . . . . . . . . . . . . . . . . 373.3.2 Permutations of two identical objects . . . . . . . . . . 373.3.3 Permutations of three identical objects . . . . . . . . . 383.3.4 Rotations of regular polygons . . . . . . . . . . . . . . 393.4 Continuous vs discrete symmetries . . . . . . . . . . . . . . . 403.5 Symmetries and Conserved Quantities:Noether's Theorem . . . . . . . . . . . . . . . . . . . . . . . . 413.6 Supplementary: Variational Mechanics and the Proof of Noether'sTheorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.6.1 Variational Mechanics: Principle of Least Action . . . . 423.6.2 Euler-Lagrange Equations . . . . . . . . . . . . . . . . 473.6.3 Proof of Noether's Theorem . . . . . . . . . . . . . . . 484 Symmetries and Linear Transformations 524.1 Learning outcomes . . . . . . . . . . . . . . . . . . . . . . . . 524.2 Review of Vectors . . . . . . . . . . . . . . . . . . . . . . . . . 534.2.1 Coordinate free denitions . . . . . . . . . . . . . . . . 534.2.2 Cartesian Coordinates . . . . . . . . . . . . . . . . . . 584.2.3 Vector operations in component form . . . . . . . . . . 594.2.4 Position vector . . . . . . . . . . . . . . . . . . . . . . 604.2.5 Dierentiation of vectors: velocity and acceleration . . 624.3 Linear Transformations . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.2 Translations . . . . . . . . . . . . . . . . . . . . . . . . 644.3.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 664.3.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 Linear Transformations and matrices . . . . . . . . . . . . . . 684.4.1 Linear transformations as matrices . . . . . . . . . . . 684.4.2 Identity Transformation and Inverses . . . . . . . . . . 704.4.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . 704.4.4 Reections . . . . . . . . . . . . . . . . . . . . . . . . . 724.4.5 Matrix Representation of Permutations of Three Objects 734.5 Pythagoras and Geometry . . . . . . . . . . . . . . . . . . . . 745 Special Relativity I: The Basics 775.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2.1 Frames5.2.2 Spacetime Diagrams . . . . . . . . . . . . . . . . . . . 785.2.3 Newtonian Relativity and Galilean Transformations . . 835.3 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.3.1 The Fundamental Postulate . . . . . . . . . . . . . . . 855.3.2 The problem with Galilean Relativity . . . . . . . . . . 855.3.3 Michelson-Morley Experiment . . . . . . . . . . . . . . 875.3.4 Maxwell's Equations . . . . . . . . . . . . . . . . . . . 905.4 Summary of Consequences . . . . . . . . . . . . . . . . . . . . 915.5 Relativity of Simultaneity . . . . . . . . . . . . . . . . . . . . 925.6 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.6.1 Derivation: . . . . . . . . . . . . . . . . . . . . . . . . 975.6.2 Proper Time . . . . . . . . . . . . . . . . . . . . . . . . 995.6.3 Experimental Conrmation . . . . . . . . . . . . . . . 1015.6.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 1025.7 Lorentz Contraction . . . . . . . . . . . . . . . . . . . . . . . 1045.7.1 Derivation . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1045.7.3 Proper Length and Proper Distance. . . . . . . . . . . 1045.7.4 Examples: . . . . . . . . . . . . . . . . . . . . . . . . . 1056 Special Relativity II: In Depth 1106.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . 1106.2.1 Derivation of general form . . . . . . . . . . . . . . . . 1106.2.2 Properties of Lorentz Transformations . . . . . . . . . 1136.2.3 Lorentzian Geometry . . . . . . . . . . . . . . . . . . . 1166.3 The Light Cone . . . . . . . . . . . . . . . . . . . . . . . . . . 1196.4 Proper time revisited . . . . . . . . . . . . . . . . . . . . . . . 1206.5 Relativistic Addition of Velocities . . . . . . . . . . . . . . . . 1226.6 Relativistic Doppler Shift . . . . . . . . . . . . . . . . . . . . . 1246.6.1 Non-relativistic Doppler Shift Review . . . . . . . . . . 1246.6.2 Relativistic Doppler Shift . . . . . . . . . . . . . . . . 1246.7 Relativistic Energy and Momentum . . . . . . . . . . . . . . . 1276.7.1 Relativistic Energy Momentum Conservation . . . . . . 1276.7.2 Relativistic Inertia . . . . . . . . . . . . . . . . . . . . 1286.7.3 Relativistic Energy . . . . . . . . . . . . . . . . . . . . 1296.7.4 Relativistic Three-Momentum . . . . . . . . . . . . . . 1296.7.5 Relationship Between Relativistic Energy and Momentum. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.7.6 Kinetic energy: . . . . . . . . . . . . . . . . . . . . . . 1306.7.7 Massless particles . . . . . . . . . . . . . . . . . . . . 1316.8 Space-time Vectors . . . . . . . . . . . . . . . . . . . . . . . . 1336.8.1 Position Four-Vector: . . . . . . . . . . . . . . . . . . . 1346.8.2 Four-momentum: . . . . . . . . . . . . . . . . . . . . . 1356.8.3 Null four-vectors . . . . . . . . . . . . . . . . . . . . . 1376.8.4 Relativistic Scattering . . . . . . . . . . . . . . . . . . 1376.8.5 More Examples . . . . . . . . . . . . . . . . . . . . . . 1386.9 Relativistic Units . . . . . . . . . . . . . . . . . . . . . . . . . 1396.10 Symmetry Redux . . . . . . . . . . . . . . . . . . . . . . . . . 1406.10.1 Matrix form of Lorentz Transformations . . . . . . . . 1406.10.2 Lorentz Transformations as a Symmetry Group . . . . 1426.11 Supplementary: Four vectors and tensors in covariant form . . 1437 General Relativity 1497.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1497.2 Problems with Newtonian Gravity . . . . . . . . . . . . . . . . 1497.2.1 Review of Newtonian Gravity . . . . . . . . . . . . . . 1497.2.2 Perihelion Shift of Mercury . . . . . . . . . . . . . . . 1517.2.3 Action at a Distance . . . . . . . . . . . . . . . . . . . 1527.2.4 The Puzzle of Inertial vs Gravitational Mass . . . . . . 1537.3 Einstein's Thinking: the Strong Principle of Equivalence . . . 1537.4 Geometry of Spacetime . . . . . . . . . . . . . . . . . . . . . . 1557.5 Some Consequences of General Relativity: . . . . . . . . . . . 1587.6 Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . 1597.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 1597.6.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . 1607.6.3 Recent Observations . . . . . . . . . . . . . . . . . . . 1617.7 Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.1 Denition . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.2 Properties: . . . . . . . . . . . . . . . . . . . . . . . . . 1637.7.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1647.7.4 Further Information . . . . . . . . . . . . . . . . . . . 1667.8 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668 Introduction to the Quantum 1708.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 1708.2 Light as particles . . . . . . . . . . . . . . . . . . . . . . . . . 1718.2.1 Review: Light as Waves . . . . . . . . . . . . . . . . . 1718.2.2 Photoelectric Eect . . . . . . . . . . . . . . . . . . . . 1718.2.3 Compton Scattering . . . . . . . . . . . . . . . . . . . 1758.3 Blackbody Radiation and the Ultraviolet Catastrophe . . . . . 1798.3.1 Blackbody Radiation . . . . . . . . . . . . . . . . . . . 1798.3.2 Derivation of Rayleigh-Jeans Law . . . . . . . . . . . . 1818.3.3 The ultraviolet catastrophe . . . . . . . . . . . . . . . 1888.3.4 Quantum resolution: . . . . . . . . . . . . . . . . . . . 1898.3.5 The Early Universe: the ultimate blackbody . . . . . . 1918.4 Particles as waves . . . . . . . . . . . . . . . . . . . . . . . . . 1968.4.1 Electron waves . . . . . . . . . . . . . . . . . . . . . . 1968.4.2 de Broglie Wavelength . . . . . . . . . . . . . . . . . . 1978.4.3 Observational Evidence . . . . . . . . . . . . . . . . . . 1998.5 The Heisenberg Uncertainty Principle . . . . . . . . . . . . . . 2029 The Wave Function 2049.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 2049.2 Quantum vs Newtonian description of physical states . . . . . 2049.2.1 Newtonian description of the state of a particle . . . . 2059.2.2 Quantum description of the state of a particle . . . . . 2059.3 Physical Consequences and Interpretation . . . . . . . . . . . 2079.4 Measurements of position . . . . . . . . . . . . . . . . . . . . 2089.5 Example: Gaussian wavefunction . . . . . . . . . . . . . . . . 2099.6 \Spooky" Action at a Distance: Non-Locality in QuantumMechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2119.6.1 The EPR \Paradox" . . . . . . . . . . . . . . . . . . . 2119.6.2 Bell's Theorem and the Experimental Repudiation ofEPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21410 The Schrodinger Equation 21710.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 21710.2 Momentum in Quantum Mechanics . . . . . . . . . . . . . . . 21810.2.1 Pure Waves . . . . . . . . . . . . . . . . . . . . . . . . 21810.2.2 The Momentum Operator . . . . . . . . . . . . . . . . 22010.3 Energy in Quantum Mechanics . . . . . . . . . . . . . . . . . 22310.4 The Time Independent Schrodinger Equation . . . . . . . . . 22410.4.1 Stationary States . . . . . . . . . . . . . . . . . . . . . 22410.4.2 The \Quantum" in Quantum Mechanics . . . . . . . . 22610.5 Examples of Stationary States . . . . . . . . . . . . . . . . . . 22610.5.1 Free particle in one dimension . . . . . . . . . . . . . . 22610.5.2 Example 2: Particle in a Box with Impenetrable Walls 22710.5.3 Example 3 : Simple Harmonic Oscillator . . . . . . . . 22910.6 Absorption and emission . . . . . . . . . . . . . . . . . . . . . 23110.7 Tunnelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23310.7.1 Tunnelling through a potential barrier of nite width . 23310.7.2 Particle in a Box with Penetrable Walls . . . . . . . . . 23510.7.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 23710.7.4 Applications of tunnelling . . . . . . . . . . . . . . . . 23810.8 The Quantum Correspondence Principle . . . . . . . . . . . . 24210.8.1 Recovering the everyday world . . . . . . . . . . . . . . 24210.8.2 The Bohr Correspondence Principle . . . . . . . . . . . 24310.9 The Time Dependent Schrodinger equation . . . . . . . . . . . 24410.9.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . 24611 The Hydrogen Atom 24911.1 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 24911.2 Newtonian (Classical) Dynamics . . . . . . . . . . . . . . . . . 24911.3 The Bohr Atom . . . . . . . . . . . . . . . . . . . . . . . . . . 25111.4 Semi-classical spectrum from the Bohr correspondence principle25411.5 Emission and Absorption Spectra . . . . . . . . . . . . . . . . 25411.6 Three Dimensional Hydrogen Atom . . . . . . . . . . . . . . . 25611.6.1 Schrodinger Equation . . . . . . . . . . . . . . . . . . . 25611.6.2 Solutions and Quantum Numbers . . . . . . . . . . . . 25811.6.3 Fermions and the spin quantum number . . . . . . . . 26211.7 Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . 26511.7.1 Hydrogen-like atoms . . . . . . . . . . . . . . . . . . . 26511.7.2 Chemical Properties and the Periodic Table . . . . . . 26612 Nuclear Physics 27012.1 Properties of the Nucleus . . . . . . . . . . . . . . . . . . . . . 27012.1.1 Mass of Nucleons . . . . . . . . . . . . . . . . . . . . . 27012.1.2 Structure of Nucleus . . . . . . . . . . . . . . . . . . . 27112.1.3 The Nuclear Force . . . . . . . . . . . . . . . . . . . . 27112.2 Binding Energy and Stability . . . . . . . . . . . . . . . . . . 27412.2.1 Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . 27412.2.2 Binding Energy . . . . . . . . . . . . . . . . . . . . . . 27512.2.3 Binding Energy per Nucleon . . . . . . . . . . . . . . . 27512.3 Formation of Elements: A Brief History of the Universe . . . . 27612.4 Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 27912.4.1 Unstable Isotopes . . . . . . . . . . . . . . . . . . . . . 27912.4.2 Neutrinos . . . . . . . . . . . . . . . . . . . . . . . . . 28112.4.3 Beta decay . . . . . . . . . . . . . . . . . . . . . . . . . 28212.4.4 Alpha Decay . . . . . . . . . . . . . . . . . . . . . . . 28312.4.5 Decay Rates . . . . . . . . . . . . . . . . . . . . . . . . 28312.4.6 Carbon Dating . . . . . . . . . . . . . . . . . . . . . . 28513 Supplementary: Advanced Topics 28713.1 Quantum Information and Quantum Computation . . . . . . . 28713.2 Relativity and quantum mechanics . . . . . . . . . . . . . . . 28714 Conclusions 28815 Appendix: Mathematical Background 28915.1 Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . . 28915.2 Probabilities and expectation values . . . . . . . . . . . . . . . 29115.2.1 Discrete Distributions . . . . . . . . . . . . . . . . . . 29115.2.2 Continuous probability distributions . . . . . . . . . . 29215.2.3 Dirac Delta Function . . . . . . . . . . . . . . . . . . . 29615.3 Supplementary: Fourier Series and Transforms . . . . . . . . . 29815.3.1 Fourier series . . . . . . . . . . . . . . . . . . . . . . . 29815.3.2 Fourier Transforms . . . . . . . . . . . . . . . . . . . . 30015.3.3 The mathematical uncertainty principle . . . . . . . . . 30215.3.4 Dirac Delta Function Revisited . . . . . . . . . . . . . 30315.3.5 Parseval's Theorem . . . . . . . . . . . . . . . . . . . . 30315.4 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30415.4.1 Moving pure waves . . . . . . . . . . . . . . . . . . . . 30415.4.2 Complex Waves . . . . . . . . . . . . . . . . . . . . . . 30515.4.3 Group velocity and phase velocity . . . . . . . . . . . 30515.4.4 Wave packets . . . . . . . . . . . . . . . . . . . . . . . 30715.4.5 Wave number and momentum . . . . . . . . . . . . . . 30915.5 Derivation of Hydrogen Wave Functions . . . . . . . . . . . . 312

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Book SynopsisIntroduction.- Notations and preliminaries.- Transformations of scalar and vector elds under the change of inertial or noninertial cartesian coordinate system.- Gravity revised.-  Maxwell equations revised.- Maxwell equations in non-inertial cartesian coordinate systems.- Scalar and vectorial electromagnetic potentials.- Lagrangian of the Electromagnetic eld.- Local gravitational time and Maxwell equations in a non-rotating coordinate system.- Motion of particles in external gravitational-electromagnetic eld.- Relation between the gravitational and inertial masses and conservation laws.- Lagrangian of the unied Gravitational-Electromagnetic eld.- Covariant formulation of the physical laws in the four-dimensional non-relativistic space-time.- Relativistic-like Dirac equation.- Thermodynamics of a moving continuum medium.- Maxwell equations in the presence of Dielectrics and/or Magnetics.- Some further consequences of Maxwell equations.- Appendix.

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Book SynopsisThe quantization of a globally hyperbolic spacetime.- Interaction of gravity with Yang-Mills and Higgs fields.- The quantum development of an asymptotically Euclidean Cauchy hypersurface.- The quantization of a Schwarzschild-AdS black hole.- The quantization of a Kerr-AdS black hole.- A partition function for quantized globally hyperbolic spacetimes with a negative cosmological constant.- Appendix.

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Book SynopsisIntroduction.- The issue of fundamental interactions.- Life and work of Antonio Aurilia.- The Physics from the electroweak to the Planck scale.- Particle sectors beyond the Standard Model.- Noncommutative and nonlocal quantum field theory.- Supergravity, superstrings and quantum gravity.- Evaporating black holes and black hole thermodynamics.- Quantum pregeometry and Planckian black holes.- Analogue gravity systems.- Higher dimensional spacetimes and terascale quantum gravity.- Dimensionally reduced Universe and Planck time cosmology.- Future perspectives.- Summary of the proposed results and potential developments.- Experimental observations in the near future.- Final remarks and conclusions.Contributors: Robert Balbinot (Bologna U. & INFN, Bologna), Patricio Gaete (CCTVal, Valparaiso & Santa Maria U., Valparaiso), José A. Helayël-Neto (Rio de Janeiro, CBPF), Robert Mann (Waterloo U. & Perimeter Inst. Theor. Phys.), Jonas Mureika (LMU, Los Angeles), Hermann Nicolai (Potsdam, MaxPlanck Inst.), Douglas Singleton (Fresno State), Anais Smailagic (INFN, Trieste), Euro Spallucci (Trieste U. & INFN, Trieste), Paul K. Townsend (Cambridge U., DAMPT).

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Book Synopsis Gravitational waves.- Ground based gravitational waves detectors.- Theory of quantum light in gravitational waves detectors.- Quantum noise reduction system overview in Advanced Virgo Plus.- Quantum noise reduction system commissioning.- Stray light in gravitational waves detectors.- Ghost beams study and mitigation.- Active control of scattered light on the FDS system.- Matching of the squeezing beam to the ITF.- New high finesse Output Mode Cleaner for Advanced Virgo Plus.

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Book SynopsisThis book offers an essential bridge between college-level introductions and advanced graduate-level books on special relativity. It begins at an elementary level, presenting and discussing the basic concepts normally covered in college-level works, including the Lorentz transformation. Subsequent chapters introduce the four-dimensional worldview implied by the Lorentz transformations, mixing time and space coordinates, before continuing on to the formalism of tensors, a topic usually avoided in lower-level courses. The book’s second half addresses a number of essential points, including the concept of causality; the equivalence between mass and energy, including applications; relativistic optics; and measurements and matter in Minkowski space-time. The closing chapters focus on the energy-momentum tensor of a continuous distribution of mass-energy and its co-variant conservation; angular momentum; a discussion of the scalar field of perfect fluids and the Maxwell field; and general coordinates.Every chapter is supplemented by a section with numerous exercises, allowing readers to practice the theory. These exercises constitute an essential part of the textbook, and the solutions to approximately half of them are provided in the appendix.Trade ReviewFrom the reviews:“The book is one of the best texts in special relativity designed for readers between the college-level and advanced level. … A number of useful and new examples is added at the end of every chapter of the book. … A very useful table of constants is added at the end of the book. … The book represents one of the best conspects in special relativity and is useful for professors of special relativity. It is good for students and every other reader.” (Alex Gaina, zbMATH, Vol. 1277, 2014)Table of ContentsFundamentals of Special Relativity.- Introduction.- The Principle of Relativity.- Groups—the Galilei group.- Galileian law of addition of velocities.- The lesson from electromagnetism.- The postulates of Special Relativity.- Consequences of the postulates.- Conclusion.- Problems.- The Lorentz transformation.- Introduction.- The Lorentz transformation.- Derivation of the Lorentz transformation.- Mathematical properties of the Lorentz transformation.- Absolute speed limit and causality.- Length contraction from the Lorentz transformation.- Time dilation from the Lorentz transformation.- Transformation of velocities and accelerations in Special Relativity.- Matrix representation of the Lorentz transformation.- The Lorentz group.- The Lorentz transformation as a rotation by an imaginary angle with imaginary time.- The GPS system.- Conclusion.- Problems.- The 4-dimensional world view.- Introduction.- The 4-dimensional world.- Spacetime diagrams.- Conclusion.- Problems.- The formalism of tensors.- Introduction.- Vectors and tensors.- Contravariant and covariant vectors.- Contravariant and covariant tensors.- Tensor algebra.- Tensor fields.- Index-free description of tensors.- The metric tensor.- The Levi-Civita symbol and tensor densities.- Conclusion.- Problems.- Tensors in Minkowski spacetime.- Introduction.- Vectors and tensors in Minkowski spacetime.- The Minkowski metric.- Scalar product and length of a vector in Minkowski spacetime.- Raising and lowering tensor indices.- Causal nature of 4-vectors.- Hypersurfaces.- Gauss’ theorem.- Conclusion.- Problems.- Relativistic mechanics.- Introduction.- Relativistic dynamics of massive particles.- The relativistic force.- Angular momentum of a particle.- Particle systems.- Conservation of mass-energy.- Conclusion.- Problems.- Relativistic optics.- Introduction.- Relativistic optics: null rays.- The drag effect.- The Doppler effect.- Aberration.- Relativistic beaming.- Visual appearance of extended objects.- Conclusion.- Problems.- Measurements in Minkowski spacetime.- Introduction.- Energy of a particle measured by an observer.- Frequency measured by an observer.- A more systematic treatment of measurement.- The 3+1 splitting.- Conclusion.- Problems.- Matter in Minkowski spacetime.- Introduction.- The energy-momentum tensor.- Covariant conservation.- Energy conditions.- Angular momentum.- Perfect fluids.- The scalar field.- The electromagnetic field.- Conclusion.- Problems.- Special Relativity in arbitrary coordinates.- Introduction.- The covariant derivative.- Spacetime curves and covariant derivative.- Physics in Minkowski spacetime revisited.- Conclusions.- Problems.- Solutions to selected problems.- References.- Index.

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Book SynopsisBeginning with an overview of the theory of black holes by the editor, this book presents a collection of ten chapters by leading physicists dealing with the variety of quantum mechanical and quantum gravitational effects pertinent to black holes. The contributions address topics such as Hawking radiation, the thermodynamics of black holes, the information paradox and firewalls, Monsters, primordial black holes, self-gravitating Bose-Einstein condensates, the formation of small black holes in high energetic collisions of particles, minimal length effects in black holes and small black holes at the Large Hadron Collider. Viewed as a whole the collection provides stimulating reading for researchers and graduate students seeking a summary of the quantum features of black holes.Table of ContentsFundamental Physics with Black Holes (Xavier Calmet).- Black holes and thermodynamics - The first half century (Daniel Grumiller, Robert McNees and Jakob Salzer).- The Firewall Phenomenon (R. B. Mann).- Monsters, Black holes and Entropy (Stephen D. H. Hsu).- Primordial Black Holes: sirens of the early Universe (Anne M. Green).- Self-gravitating Bose-Einstein condensates (Pierre-Henri Chavanis).- Quantum Amplitudes in Black-Hole Evaporation with Local Supersymmetry (P.D.D'Eath and A.N.St.J.Farley).- Hawking radiation from higher-dimensional black holes (Panagiota Kanti and Elizabeth Winstanley).- Black Holes at the Large Hadron Collider (Greg Landsberg).- Minimum length effects in black hole physics (Roberto Casadio, Octavian Micu, Piero Nicolini).

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Book SynopsisThis book, now in its second edition, provides an introductory course on theoretical particle physics with the aim of filling the gap that exists between basic courses of classical and quantum mechanics and advanced courses of (relativistic) quantum mechanics and field theory. After a concise but comprehensive introduction to special relativity, key aspects of relativistic dynamics are covered and some elementary concepts of general relativity introduced. Basics of the theory of groups and Lie algebras are explained, with discussion of the group of rotations and the Lorentz and Poincaré groups. In addition, a concise account of representation theory and of tensor calculus is provided. Quantization of the electromagnetic field in the radiation range is fully discussed. The essentials of the Lagrangian and Hamiltonian formalisms are reviewed, proceeding from systems with a finite number of degrees of freedom and extending the discussion to fields. The final four chapters are devoted to development of the quantum field theory, ultimately introducing the graphical description of interaction processes by means of Feynman diagrams. The book will be of value for students seeking to understand the main concepts that form the basis of contemporary theoretical particle physics and also for engineers and lecturers. An Appendix on some special relativity effects is added.Trade Review“This book originates from a course on advanced quantum mechanics given by the author at the Politechnico Turin for students of physical engineering to provide them with some insight into modern fundamental physics. … This book not merely gives some insight into modern fundamental physics but also renders a good fundament for further studies of quantum field theory and elementary article physics in that correct suggestions are mediated.” (K.-E. Hellwig, zbMATH 1371.81001, 2017)Table of ContentsSpecial Relativity.- Relativistic Dynamics.- The Equivalence Principle.- The Poincaré Group.- Maxwell Equations and Special Relativity.- Quantization of the Electromagnetic Field.- Group Representations and Lie Algebras.- Lagrangian and Hamiltonian Formalism.- Quantum Mechanics Formalism.- Relativistic Wave Equations.- Quantization of Boson and Fermion Fields.- Fields in Interaction.

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Book SynopsisBryce DeWitt, a student of Nobel Laureate Julian Schwinger, was himself one of the towering figures in 20th century physics, particularly renowned for his seminal contributions to quantum field theory, numerical relativity and quantum gravity. In late 1971 DeWitt gave a course on gravitation at Stanford University, leaving almost 400 pages of detailed handwritten notes. Written with clarity and authority, and edited by his former student Steven Christensen, these timeless lecture notes, containing material or expositions not found in any other textbooks, are a gem to be discovered or re-discovered by anyone seriously interested in the study of gravitational physics.Trade ReviewFrom the reviews:“DeWitt’s lectures cover interesting and detailed material which is rarely found in other text books. It is a book for the advanced reader.” (Norbert Dragon, General Relativity and Gravitation, Vol. 44, 2012)Table of ContentsReview of the Uses of Invariants in Special Relativity.- Accelerated Motion in Special Relativity.- Realization of Continuous Groups.- Riemannian Manifolds.- The Free Particle Geodesics.- Weak Field Approximation. Newton`s Theory.- Ensembles of Particles.- Production of Gravitational Fields by Matter.- Conservation Laws.- Phenomenological Description of a Conservative Continuous Medium.- Solubility of the Einstein and Matter Equations.- Energy, Momentum and Stress in the Gravitational Field.- Measurement of Asymptotic Field.- The Electromagnetic Field.- Gravitational Waves.- Spinning Bodies.- Weak Field Gravitational Wave.- Stationary Spherically (or Rotationally) Symmetric Metric.- Kerr Metric Subcalculations.- Friedmann Cosmology.- Dynamical Equations and Diffeomorphisms.

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Book SynopsisBlack Holes are still considered to be among the most mysterious and fascinating objects in our universe. Awaiting the era of gravitational astronomy, much progress in theoretical modeling and understanding of classical and quantum black holes has already been achieved. The present volume serves as a tutorial, high-level guided tour through the black-hole landscape: information paradox and blackhole thermodynamics, numerical simulations of black-hole formation and collisions, braneworld scenarios and stability of black holes with respect to perturbations are treated in great detail, as is their possible occurrence at the LHC. An outgrowth of a topical and tutorial summer school, this extensive set of carefully edited notes has been set up with the aim of constituting an advanced-level, multi-authored textbook which meets the needs of both postgraduate students and young researchers in the fields of modern cosmology, astrophysics and (quantum) field theory. Table of ContentsBlack Holes and their Properties.- What Exactly is the Information Paradox?.- Classical Yang–Mills Black Hole Hair in Anti-de Sitter Space.- Black Hole Thermodynamics and Statistical Mechanics.- Colliding Black Holes and Gravitational Waves.- Numerical Simulations of Black Hole Formation.- Higher-Dimensional Black Holes.- Black Holes in Higher-Dimensional Gravity.- Braneworld Black Holes.- Higher Order Gravity Theories and Their Black Hole Solutions.- Gravitational Waves from Braneworld Black Holes.- Black Holes at the Large Hadron Collider.- Perturbations of Black Holes.- Perturbations and Stability of Higher-Dimensional Black Holes.- Analytic Calculation of Quasi-Normal Modes.

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Book SynopsisThis book is aimed at theoretical as well as primarily physicists graduate students in field working quantum theory, quantum gravity, theories, gauge to sdme and and, it is not extent, general relativity cosmology. Although aimed at a I that it also be of level, hope in mathematically rigorous may terest to mathematical and mathematicians in physicists working spectral of differential mani geometry, spectral asymptotics on operators, analysis differential and mathematical methods in folds, geometry quantum theory. Thisbook will be considered too abstract some but certainly by physicists, not detailed and most mathematicians. This in completeenoughby means, thatthe material is at the level of particular, presented "physical" So, rigor. there theorems and areno and technicalcalculationsare lemmas, proofs long omitted. I tried detailed to a ofthe basic Instead, give presentation ideas, methodsandresults. Itried makethe to as andcom Also, exposition explicit as the lessabstractandhaveillustratedthe plete possible, methods language and results withsome As is well "onecannot examples. known, cover every in an text. The in this thing", especially introductory approach presented book the lines is a further of the so called along goes (and development) fieldmethod ofDe Witt. As a Ihavenot dealt at background consequence, allwithmanifoldswith boundary,non Laplacetype (ornonminimal) opera Riemann Cartan manifolds well with as as recent tors, developments many and advanced such Ashtekar's more as topics, approach,supergravity,strings, matrix etc. The membranes, interested reader is referred models, M theory tothe literature.Trade Review"This monograph rightly belongs to a series ‘Lecture notes in Physics’, as it represents a well-written review of main results by the author, who is a recognized expert on heat kernel techniques in quantum gravity. [...] The results exposed in this book reflect the major contributions of the author to differential geometry and the theory of differential operators. They have many applications in quantum field theory with background fields, and indeed, the book can be used as a text for a short graduate course in the heat kernel techniques and their quantum gravity." (Mathematical Reviews 2003a)Table of ContentsBackground Field Method in Quantum Field Theory.- Technique for Calculation of De Witt Coefficients.- Partial Summation of Schwinger-De Witt Expansion.- Higher-Derivative Quantum Gravity.- Conclusion.

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Book SynopsisThe idea to hold a workshop on globular clusters in Concepcion emerged during 2005 out of a variety of circumstances. Four years had passed since the IAUSymposium 207 onExtragalactic Globular Clusters inPuc' on, atime span, which we thought to be long enough for justifying a new meeting with theintent toreviewthemostrecentdevelopments inthe?eld of extragalactic stars clusters. Originally intended to be a small-scale workshop, the response from the community was overwhelming so that only a full-scale international conferencewas abletocopewith thenumerousrequestsfortalksandposters. Finally, about 160 participants gathered in Concepci' on on March 6th, 2006. The venue was the university lecture hall located in the facultad de - manidadesyartesoftheUniversidaddeConcepci' on.Posterswereexposedin the lobby of the faculty building. The weather was as good as one can reas- ablyexpectfromalatesummerinConcepci' on.Althoughtheprogrammewas so tight that separate poster sessions other than those during co?ee breaks could not be accomodated, posters received a lot of attention. From the ?rst to the last talk, the atmosphere was inspiring and the conference could keep its tension for ?ve full days. This clearly shows that the attraction which globular clusters exercise on astrophysicists of quite di?erent ?avours, is as strong as ever.Table of ContentsDetailed Studies of Individual Globular Clusters.- Detailed Chemical Abundances of Extragalactic Globular Clusters.- Spectroscopic Abundances and Radial Velocities of the Galactic Globular Clusters 2MASS GC01 and 2MASS GC02: Preliminary Results.- Abundance Anomalies in Galactic Globular Clusters – Looking for the Stellar Culprits.- Globular Clusters in the Direction of the Inner Galaxy.- Globular Cluster Research with Astronomical Archives.- Super-He-Rich Populations in Globular Clusters.- Testing the BH 176 and Berkeley 29 Association with GASS/Monoceros.- New Yonsei-Yale (Y 2) Isochrones and Horizontal-Branch Evolutionary Tracks with Helium Enhancements.- Search for Candle Stars in Globular Clusters: Spectroscopic Analysis of Post-AGB Candidates.- The Lack of Binaries Among Hot Horizontal Branch Stars: M80 and NGC5986.- Semi-Empirical Determination of the Mass Distribution of Horizontal Branch Stars in M3.- The Most Massive Clusters.- Globular Clusters, Galactic Nuclei and Supermassive Black Holes.- UCDs – A Mixed Bag of Objects.- Ultra-Compact Dwarf Galaxies and Globular Clusters: A Review of Their Spatial and Dynamical Properties.- The Maximum Mass of Star Clusters.- The Stellar Population of Ultra-Compact Dwarf Galaxies.- News on Ultra-Compact Dwarfs and Blue Globular Clusters.- UCDs and GCs: Structural Differences from HST Imaging.- Ultra-Compact Stellar Systems in the Fornax Galaxy Cluster.- Multi-Colour Imaging of Ultra-Compact Objects in the Fornax Cluster.- Young Star Clusters.- Hierarchical Formation of Galactic Clusters.- Young Massive Clusters – Formation Efficiencies and (Initial) Mass Functions.- The Radii of Thousands of Star Clusters in M51 with HST/ACS.- Extragalactic Star Clusters in Merging Galaxies.- The Environment of Young Massive Clusters.- Star/Cluster Formation in Complexes: Insights from IFUs and HST.- Spectral Evolution of Blue Concentrated Star Clusters in the Large Magellanic Cloud.- Young Star Clusters in the SMC.- Molecular Clouds and Star Formation in the Magellanic System by NANTEN.- Two Star Cluster Populations in NGC 45.- Characterization of Open Cluster Remnants.- HST Photometry of the Binary Globular Cluster Sersic 13N-S in NGC5128[1].- Globular Cluster Systems in Dwarf and Irregular Galaxies.- LMC Cluster Abundances and Kinematics.- Globular Clusters in Dwarf Galaxies.- Globular Clusters in Dwarf and Giant Galaxies.- The Age-Metallicity Relation of the SMC.- Integrated Spectroscopic Analysis of Galactic and Small Magellanic Cloud Clusters.- Variable Stars in the Globular Clusters and in the Field of the Fornax dSph Galaxy.- Physical Parameters of Intermediate-Age LMC Clusters from Modelling of HST CMDs.- RGB Properties of the LMC/SMC Clusters in the Infrared.- WLM-1: A Non-Rotating, Gravitationally Unperturbed, Highly Elliptical Extragalactic Globular Cluster.- Globular Cluster Systems in Spiral Galaxies.- Star Clusters in M33 – Clues to Galaxy Formation and Evolution.- M31 and its Globular Clusters.- IR Integrated Light Colors For Galactic GCs and An Update on Young M31 Globular Clusters.- Nuclear Star Clusters in Edge-on Galaxies.- HST ACS Wide-Field Photometry of the Sombrero Galaxy Globular Cluster System.- Intermediate-Age Globular Clusters in M31.- Metal-Poor Globular Clusters of the Galactic Bulge.- Globular Cluster System and Milky Way Properties Revisited.- RR Lyrae-Based Calibration of the Globular Cluster Luminosity Function.- Globular Cluster Systems in Spiral Galaxies Using ACS Imaging.- Laser Guide Star Imaging of M31 Globulars.- GALEX UV Observations of M31 Globular Clusters.- Integrated Spectroscopy of Galactic Globular Clusters.- Globular Cluster Systems in Early-Type Galaxies.- Globular Cluster Systems: Do They Really Trace Star Formation? (Or Rather: What Mode of Star Formation Do They Trace?).- Globular Clusters in Early Type Galaxies.- Globular Clusters and Galaxy Formation.- Globular Cluster Systems in Giant Ellipticals: New and Old Patterns.- The ACS Virgo Cluster Survey.- Globular Clusters at the Centre of the Fornax Cluster: Tracing Interactions Between Galaxies.- Globular Cluster Bimodality Revisited (and the Globulars-Galaxy Halo Connection).- Globular Cluster Systems, Diffuse Star Clusters, and Host Galaxies in the ACS Virgo Cluster Survey.- Hot Populations in M87 Globular Clusters.- A Subaru/Suprime-Cam Wide-Field Survey of Globular Cluster Populations around M87.- Stellar Populations of Globular Clusters in NGC 1407.- The Globular Cluster System of NGC 5846 Revisited: Colours, Sizes and X-Ray Counterparts.- Globular Cluster Systems in Shell Ellipticals.- GMOS Photometry of Five Globular Cluster Systems: NGC 4649, NGC 3923, NGC 524, NGC 3115 and NGC 3379.- Structural Parameters from Ground-based Observations of Globular Clusters in NGC 5128.- Globular Cluster Populations in Early-Type Galaxies.- The Low-Mass X-Ray Binary Globular Cluster Connection in the ACS Virgo Cluster Survey.- The Globular Cluster System of NGC 5128: Combining Broad-Band Color and Lick Index Analysis.- The Galaxy – Globular Cluster Connection in NGC 3115.- Velocity Dispersions of Bright Globular Clusters in NGC 5128.- Evolution of Cluster Systems and their Host Galaxies.- Imprint of Galaxy Formation and Evolution on Globular Cluster Properties.- Formation of Globular Clusters in Hierarchical Cosmology: ART and Science.- Globular Cluster Formation in Mergers.- The Formation Histories of Metal-Rich and Metal-Poor Globular Clusters.- Globular Cluster System Evolution in Early Type Galaxies.- Star Cluster Evolution: From Young Massive Star Clusters to Old Globulars.- A Wide-Field Survey of the Globular Cluster Systems of Giant Galaxies.- IGCs in the Virgo Cluster.- A New Explanation of Globular Cluster Color Distributions.- Formation of Intracluster and Intercluster Globular Clusters.- The Effect of Giant Molecular Clouds on Star Clusters.- Metal-rich Globular Clusters: An Unaccounted Factor Responsible for Their Formation?.- On the Globular Cluster Color Distributions.- Dynamical Evolution of Star Clusters.- Dissolution of Globular Clusters.- Dynamical Masses of Young Star Clusters: Constraints on the Stellar IMF and Star-Formation Efficiency.- Dynamical Evolution of Rotating Globular Clusters with Embedded Black Holes.- The Dynamical Evolution of Young Clusters and Galactic Implications.- Simulations of Globular Clusters Merging in Galactic Nuclear Regions.- The Origin of the Gaussian Initial Mass Function of Globular Cluster Systems.- Evolution of Globular Cluster Systems.- Tidal Disruption and the Tale of Three Clusters.- Tidal Tails Around Globular Clusters: Are they Good Tracers of Cluster Orbits?.- Modelling the Tidal Tails of NGC 5466.- The Search for Tidal Tails of Globular Clusters: NGC4147.- Internal Rotation of Young Globular Clusters.- Mass Segregation in Young Star Clusters.- Dynamics of Globular Cluster Systems.- Kinematics of Globular Cluster Systems.- Dark Matter in the Elliptical Galaxies NGC 1399 and NGC 4636.- Ages, Abundances, and Kinematics of Globular Clusters in NGC 3379 and NGC 4649 with Gemini/GMOS.- The Dark Halo of NGC 1399 and MOND.- Dynamics of the Globular Cluster System of NGC 5128.- Open Questions in the Globular Cluster – Galaxy Connection.- Open Questions in the Globular Cluster – Galaxy Connection.

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Book SynopsisThis book provides an original introduction to the geometry of Minkowski space-time. A hundred years after the space-time formulation of special relativity by Hermann Minkowski, it is shown that the kinematical consequences of special relativity are merely a manifestation of space-time geometry.The book is written with the intention of providing students (and teachers) of the first years of University courses with a tool which is easy to be applied and allows the solution of any problem of relativistic kinematics at the same time. The book treats in a rigorous way, but using a non-sophisticated mathematics, the Kinematics of Special Relativity. As an example, the famous "Twin Paradox" is completely solved for all kinds of motions.The novelty of the presentation in this book consists in the extensive use of hyperbolic numbers, the simplest extension of complex numbers, for a complete formalization of the kinematics in the Minkowski space-time.Moreover, from this formalization the understanding of gravity comes as a manifestation of curvature of space-time, suggesting new research fields.Table of ContentsIntroduction.- Hyperbolic Numbers.- Geometrical Representation of Hyperbolic Numbers.- Trigonometry in the Hyperbolic (Minkowski) Plane.- Equilateral Hyperbolas and Triangles in the Hyperbolic Plane.- The Motions in Minkowski Space-Time (Twin Paradox).- Some Final Considerations.

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Book SynopsisThis graduate-level, course-based text is devoted to the 3+1 formalism of general relativity, which also constitutes the theoretical foundations of numerical relativity. The book starts by establishing the mathematical background (differential geometry, hypersurfaces embedded in space-time, foliation of space-time by a family of space-like hypersurfaces), and then turns to the 3+1 decomposition of the Einstein equations, giving rise to the Cauchy problem with constraints, which constitutes the core of 3+1 formalism. The ADM Hamiltonian formulation of general relativity is also introduced at this stage. Finally, the decomposition of the matter and electromagnetic field equations is presented, focusing on the astrophysically relevant cases of a perfect fluid and a perfect conductor (ideal magnetohydrodynamics). The second part of the book introduces more advanced topics: the conformal transformation of the 3-metric on each hypersurface and the corresponding rewriting of the 3+1 Einstein equations, the Isenberg-Wilson-Mathews approximation to general relativity, global quantities associated with asymptotic flatness (ADM mass, linear and angular momentum) and with symmetries (Komar mass and angular momentum). In the last part, the initial data problem is studied, the choice of spacetime coordinates within the 3+1 framework is discussed and various schemes for the time integration of the 3+1 Einstein equations are reviewed. The prerequisites are those of a basic general relativity course with calculations and derivations presented in detail, making this text complete and self-contained. Numerical techniques are not covered in this book.Trade ReviewFrom the reviews:“The monograph originating from lectures is devoted to the 3+1 formalism in general relativity. It starts with three chapters on basic differential geometry, the geometry of single hypersurfaces embedded in space-time, and the foliation of space-time by a family of spacelike hypersurfaces. … With the attempt to make the text self-consistent and complete, the calculations are … detailed such that the book is well suitable for undergraduate and graduate students.” (Horst-Heino von Borzeszkowski, Zentralblatt MATH, Vol. 1254, 2013)“This book is written for advanced students and researchers who wish to learn the mathematical foundations of various approaches that have been proposed to solve initial value problems (with constraints) for the Einstein equations numerically. … Even for experts it may be useful, as it includes an extensive bibliography up to 2011.” (Hans-Peter Künzle, Mathematical Reviews, January, 2013)Table of ContentsBasic Differential Geometry.- Geometry of Hypersurfaces.- Geometry of Foliations.- 3+1 decomposition of Einstein Equation.- 3+1 Equations for Matter and Electromagnetic Field.- Conformal Decompositon.- Asymptotic Flatness and Global Quantities.- The Initial Data Problem.- Choice of Foliation and Spatial Coordiinates.- Evolution Schemes.- Conformal Killing Operator and Conformal Vector Laplacian.- Sage Codes.

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Book SynopsisSome major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as.Trade ReviewFrom the reviews:“This book in part is about on some technology concerning the local zeta function applied to quantum field theory in curved static (thermal) spacetime to regularize the stress energy tensor and the field fluctuations. … I find this book extremely useful and important, because it signifies the beauty of a mathematical technique in physics in general. I recommend this book for you it is an amazing reading!” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, January, 2014)Table of ContentsPart I QFT and the Casimir Effect.- 1. I. Ya. AREF’EVA. Colliding Hadrons as Cosmic Membranes and Possible Signatures of Lost Momentum.- 2. M. ASOREY, I. Cavero‐Peláez and J. M. Muñoz‐Casta. Vacuum energy and the Topology of the Universe.-3. M. BORDAG and I. Pirozhenko. The Low Temperature Corrections to the Casimir Force Between a Sphere and a Plane.- 4. I. BREVIK. Casimir Effect for the Piecewise Uniform String.- 5. I.L. BUCHBINDER, N.G. Pletnev and I.B. Samsonov. N = 2 and N = 4 Supersymmetric Low‐Energy Effective Actions in Three Dimensions.- 6. M. CHAICHIAN. Colour Confinement, the Goto‐Imamura‐Schwinger Term and Renormalization Group.- 7. J. GOMIS. Non‐Central Extensions of (Super) Poincaré Algebra and (Susy) Electromagnetic Backgrounds.- 8. K. A. MILTON, J. Wagner, P. Parashar, I. Cavero‐Peláez, I. Brevik and S. A. Ellingsen. Multiple Scattering: Dispersion, Temperature Dependence, and Annular Pistons.- Part II Gravity and Cosmology.- 9. M. BOUHMADI‐LÓPEZ. Brane Cosmology with an f(R)‐Contribution.- 10. S. CAPOZZIELLO. f(R)‐Gravity Matched with Large Scale Structure and Cosmological Observations.- 11. S. CARLONI. An Analysis of the Phase Space of Hořava‐Lifshitz Cosmologies.- 12. C. CORDA. Gravitational Waves Astronomy: a Cornerstone for Gravitational Theories.- 13. R. DI CRISCIENZO, L. Vanzo and S. Zerbini. Hamilton‐Jacobi Method and Gravitation.- 14. K. N. Ananda, S. Carloni and P. K. S. DUNSBY. A Characteristic Signature of Fourth Order Gravity.- 15. V. FARAONI. Horizons and Singularity in Clifton's Spherical Solution of f(R)‐vacuum.- 16. R. GARATTINI. Gravitational Zero Point Energy and the Induced Cosmological Constant.- 17. P. GONZALEZ‐DÍAZ. Lensing Effects in Ringholes and the Multiverse Black Holes.- 18. L. LUSANNA. Hamiltonian ADM Gravity in Non‐Harmonic Gauges with Well Defined Non‐Euclidean 3‐Spaces: How Much Darkness can be Explained as a Relativistic Inertial Effect?- 19. J. Beltrán and A. LÓPEZ MAROTO. Dark Energy and Cosmic Magnetic Fields: Electromagnetic Relics from Inflation.- 20. N. Carlevaro, G. MONTANI and M. Lattanzi. On the Viability of Non‐Analytical f(R)‐Theory.- 21. S. NOJIRI. Towards the Unification of Late‐Time Acceleration and Inflation by k‐Essence Model.- 22. N. Deruelle and M. SASAKI. Conformal Equivalence in Classical Gravity: the Example of “Veiled” General Relativity.- 23. L. SEBASTIANI. Finite‐Time Singularities in Modified f(R;G)‐Gravity and Singularity Avoidance.- 24. P. J. SILVA. Asymptotic Darkness in Hořava‐Lifshitz Gravity.- 25. C. F. SOPUERTA and N. Yunes. Testing Modified Gravity with Gravitational Wave Astronomy.- 26. P. K. TOWNSEND. Gravitons in Flatland.- 27. M. M. Sheikh‐Jabbari and A. TUREANU. Very Special Relativity and Noncommutative Space‐Time.- Part III Zeta Functions in Physics and Mathematics.-28. G. Fucci, K. KIRSTEN and P. Morales. Pistons Modelled by Potentials.- 29. V. Moretti. Local ζ‐functions, stress‐energy tensor, field fluctuations, and all that, in curved static spacetime.- 30. V. Muñoz and R. PÉREZ‐MARCO. Ergodic Solenoidal Geometry.- 31. A. VOROS. Zeta‐Regularization and Exact WKB Method for a General 1D Schrödinger equation.- 32. G. Cognola and S. ZERBINI. Generalized Zeta Function Regularization and the Multiplicative Anomaly.- Part IV Non‐standard approaches.- 33. R. M. SANTILLI. Isominkowskian Geometry for Interior Dynamical Problems.- 34. L. YING. Nuclear Fusion Drives Cosmic Expansion.- Index

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Book SynopsisIt would seem that any specialist in plasma physics studying a medium in which the interaction between particles is as distance-dependent as the inter­ action between stars and other gravitating masses would assert that the role of collective effects in the dynamics of gravitating systems must be decisive. However, among astronomers this point of view has been recog­ nized only very recently. So, comparatively recently, serious consideration has been devoted to theories of galactic spiral structure in which the dominant role is played by the orbital properties of individual stars rather than collec­ tive effects. In this connection we would like to draw the reader's attention to a difference in the scientific traditions of plasma physicists and astrono­ mers, whereby the former have explained the delay of the onset of controlled thermonuclear fusion by the "intrigues" of collective processes in the plasma, while many a generation of astronomers were calculating star motions, solar and lunar eclipses, and a number of other fine effects for many years ahead by making excellent use of only the laws of Newtonian mechanics. Therefore, for an astronomer, it is perhaps not easy to agree with the fact that the evolution of stellar systems is controlled mainly by collective effects, and the habitual methods of theoretical mechanics III astronomy must make way for the method of self-consistent fields.Table of Contents(Volume I).- § 1. Basic Concepts and Equations of Theory.- § 2. Equilibrium States of Collisionless Gravitating Systems.- § 3. Small Oscillations and Stability.- §4. Jeans Instability of a One—Component Uniform Medium.- §5. Jeans Instability of a Multicomponent Uniform Medium.- 5.1. Basic Theorem (on the Stability of a Multicomponent System with Components at Rest).- 5.2. Four Limiting Cases for a Two—Component Medium.- 5.3. Table of Jeans Instabilities of a Uniform Two—Component Medium.- 5.4. General Case of n Components.- §6. Non—Jeans Instabilities.- § 7. Qualitative Discussion of the Stability of Spherical, Cylindrical (and Disk—Shaped) Systems with Respect to Radial Perturbations.- I Theory.- I Equilibrium and Stability of a Nonrotating Flat Gravitating Layer.- § 1. Equilibrium States of a Collisionless Flat Layer.- § 2. Gravitational (Jeans) Instability of the Layer.- § 3. Anisotropic (Fire—Hose) Instability of a Collisionless Flat Layer.- 3.1. Qualitative Considerations.- 3.2. Derivation of the Dispersion Equation for Bending Perturbations of a Thin Layer.- 3.3. Fire—Hose Instability of a Highly Anisotropic Flat Layer.- 3.4. Analysis of the Dispersion Equation.- 3.5. Additional Remarks.- § 4. Derivation of Integra—Differential Equations for Normal Modes of a Flat Gravitating Layer.- § 5. Symmetrical Perturbations of a Flat Layer with an Isotropic Distribution Function Near the Stability Boundary.- § 6. Perpendicular Oscillations of a Homogeneous Collisionless Layer.- 6.1. Derivation of the Characteristic Equation for Eigenfrequencies.- 6.2. Stability of the Model.- 6.3. Permutational Modes.- 6.4. Time—Independent Perturbations (? = 0).- Problems.- II Equilibrium and Stability of a Collisionless Cylinder.- §1. Equilibrium Cylindrical Configurations.- § 2. Jeans Instability of a Cylinder with Finite Radius.- 2.1. Dispersion Equation for Eigenfrequencies of Axial-Symmetrical Perturbations of a Cylinder with Circular Orbits of Particles.- 2.2. Branches of Axial—Symmetrical Oscillations of a Rotating Cylinder with Maxwellian Distribution of Particles in.- 2.3. Longitudinal Velocities.- 2.4. Oscillative Branches of the Rotating Cylinder with a Jackson Distribution Function (in Longitudinal Velocities).- 2.5. Axial—Symmetrical Perturbations of Cylindrical Models of a More General Type.- § 3. Nonaxial Perturbations of a Collisionless Cylinder.- 3.1. The Long—Wave Fire-Hose Instability.- 3.2. Nonaxial Perturbations of a Cylinder with Circular Particle Orbits 100§ 4. Stability of a Cylinder with Respect to Flute—like Perturbations.- § 5. Local Analysis of the Stability of Cylinders (Flute—like Perturbations).- 5.1. Dispersion Equation for Model (2), § 1.- 5.2. Maxwellian Distribution Function.- § 6. Comparison with Oscillations of an Incompressible Cylinder.- 6.1. Flute—like Perturbations (kz = 0).- § 7. Flute—like Oscillations of a Nonuniform Cylinder with Circular Orbits of Particles.- Problems.- III Equilibrium and Stability of Collisionless Spherically Symmetrical Systems.- § 1. Equilibrium Distribution Functions.- § 2. Stability of Systems with an Isotropic Particle Velocity Distribution.- 2.1. The General Variational Principle for Gravitating Systems with the Isotropic Distribution of Particles in Velocities (f0 = f0(E), f’0 = df0|dE ? 0).- 2.2. Sufficient Condition of Stability.- 2.3. Other Theorems about Stability. Stability with Respect to Nonradial Perturbations.- 2.4. Variational Principle for Radial Perturbations.- 2.5. Hydrodynamical Analogy.- 2.6. On the Stability of Systems with Distribution Functions That Do Not Satisfy the Condition f’0 (E) ? 0.- § 3. Stability of Systems of Gravitating Particles Moving On Circular Trajectories.- 3.1. Stability of a Uniform Sphere.- 3.2. Stability of a Homogeneous System of Particles with Nearly Circular Orbits.- 3.3. Stability of a Homogeneous Sphere with Finite Angular Momentum.- 3.4. Stability of Inhomogeneous Systems.- § 4. Stability of Systems of Gravitating Particles Moving in Elliptical Orbits.- 4.1. Stability of a Sphere with Arbitrary Elliptical Particle Orbits.- 4.2. Instability of a Rotating Freeman Sphere.- § 5. Stability of Systems with Radial Trajectories of Particles.- 5.1. Linear Stability Theory.- 5.2. Simulation of a Nonlinear Stage of Evolution.- § 6. Stability of Spherically Symmetrical Systems of General Form.- 6.1. Series of the Idlis Distribution Functions.- 6.2. First Series of Camm Distribution Functions (Generalized Poly tropes).- 6.3. Shuster’s Model in the Phase Description.- §7. Discussion of the Results.- Problems.- IV Equilibrium and Stability of Collisionless Ellipsoidal Systems.- § 1. Equilibrium Distribution Functions.- 1.1 Freeman’s Ellipsoidal Models.- 1.2. “Hot” Models of Collisionless Ellipsoids of Revolution.- § 2. Stability of a Three—Axial Ellipsoid and an Elliptical Disk.- 2.1. Stability of a Three-Axial Ellipsoid.- 2.2. Stability of Freeman Elliptical Disks.- § 3. Stability of Two—Axial Collisionless Ellipsoidal Systems.- 3.1. Stability of Freeman’s Spheroids.- 3.2. Peebles—Ostriker Stability Criterion. Stability of Uniform Ellipsoids, “Hot” in the Plane of Rotation.- 3.3. The Fire-Hose Instability of Ellipsoidal Stellar Systems.- 3.4. Secular and Dynamical Instability. Characteristic Equation for Eigenfrequencies of Oscillations of Maclaurin Ellipsoids.- Problems.- V Equilibrium and Stability of Flat Gravitating Systems.- § 1. Equilibrium States of Flat Gaseous and Collisionless Systems.- 1.3. Systems with Circular Particle Orbits.- 1.4. Plasma Systems with a Magnetic Field.- 1.5. Gaseous Systems.- 1.6. “Hot” Collisionless Systems.- § 2. Stability of a “Cold” Rotating Disk.- 2.1. Membrane Oscillations of the Disk.- 2.2. Oscillations in the Plane of the Disk.- § 3. Stability of a Plasma Disk with a Magnetic Field.- 3.1. Qualitative Derivation of the Stability Condition.- 3.2. Variational Principle.- 3.3. Short—Wave Approximation.- 3.4. Numerical Analysis of a Specific Model.- § 4. Stability of a “Hot” Rotating Disk.- 4.1. Oscillations in the Plane of the Disk.- 4.2. Bending Perturbations.- 4.3. Methods of the Stability Investigation of General Collisionless Disk Systems.- 4.4. Exact Spectra of Small Perturbations.- 4.5. Global Instabilities of Gaseous Disks. Comparison of Stability Properties of Gaseous and Stellar Disks.- Problems.- References.- Additional References.

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Table of Contents(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- § 1. Beam Instability of a Gravitating Medium.- 1.1. Theorem of a Number of Instabilities of the Heterogeneous System with Homogeneous Flows.- 1.2. Expression for the Growth Rate of the Kinetic Beam Instability in the Case of a Beam of Small Density (for an Arbitrary Distribution Function).- 1.3. Beam with a Step Function Distribution.- 1.4. Hydrodynamical Beam Instability. Excitation of the Rotational Branch.- 1.5. Stabilizing Effect of the Interaction of Gravitating Cylinders and Disks.- 1.6. Instability of Rotating Inhomogeneous Cylinders with Oppositely Directed Beams of Equal Density.- § 2. Gradient Instabilities of a Gravitating Medium.- 2.1. Cylinder of Constant Density with Radius-Dependent Temperature. Hydrodynamical Instability.- 2.2. Cylinder of Constant Density with a Temperature Jump. Kinetic Instability.- 2.3. Cylinder with Inhomogeneous Density and Temperature.- § 3. Hydrodynamical Instabilities of a Gravitating Medium with a Growth Rate Much Greater than that of Jeans.- 3.1. Hydrodynamical Instabilities in the Model of a Flat Parallel Flow.- 3.2. Hydrodynamical Instabilities of a Gravitating Cylinder.- §4. General Treatment of Kinetic Instabilities.- 4.1. Beam Effects in the Heterogeneous Model of a Galaxy.- 4.2. Influence of a “Black Hole” at the Center of a Spherical System on the Resonance Interactions Between Stars and Waves.- 4.3. Beam Instability in the Models of a Cylinder and a Flat Layer.- VII Problems of Nonlinear Theory.- § 1. Nonlinear Stability Theory of a Rotating, Gravitating Disk.- 1.1. Nonlinear Waves and Solitons in a Hydrodynamical Model of an Infinitely Thin Disk with Plane Pressure.- 1.2. Nonlinear Waves in a Gaseous Disk.- 1.3. Nonlinear Waves and Solitons in a Stellar Disk.- 1.4. Explosive Instability.- 1.5. Remarks on the Decay Processes.- 1.6. Nonlinear Waves in a Viscous Medium.- § 2. Nonlinear Interaction of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- § 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- § 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- §5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- § 1. Oort’s Antievolutionary Hypothesis.- § 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- § 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- § 4. Lynden-Bell’s Collisionless Relaxation.- § 5. Estimates of “Collisionlessness” of Particles in Different Real Systems.- IX Spherical Systems.- § 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- § 2. Classification of Unstable Modes in Scales.- § 3. Universal Criterion of the Instability.- § 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the System’s Evolution.- § 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- § 6. Example of Strongly Unstable Model.- § 7. Can Lynden-Bell’s Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- § 8. Is the “Unstable” Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a “Black Hole”?.- X Ellipsoidal Systems.- § 1. Objects Under Study.- § 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the Observed Oblatenesses of S- and SO-Galaxies with the Oblateness of E-Galaxies.- 2.3. Two Possible Solutions of the Problem.- 2.4. The Boundary of the Anisotropic (Fire-Hose) Instability Determines the Critical Value of Oblateness.- 2.5. Universal Criterion of Instability.- §3. SB-Galaxies.- 3.1. The Main Problem.- 3.2. Detection in NGC 4027 of Counterflows as Predicted by Freeman.- 3.3. Stability of Freeman Models of SB-Galaxies with Observed Oblateness.- XI Disk-like Systems. Spiral Structure.- § 1. Different Points of View on the Nature of Spiral Structure.- § 2. Resonant Interaction of the Spiral Wave with Stars of the Galaxy.- 2.1. Derivation of Expressions for the Angular Momentum and Energy of the Spiral Wave.- 2.2. Physical Mechanisms of Energy and Angular Momentum Exchange Between the Spiral Waves and the Resonant Stars.- § 3. The Linear Theory of Stationary Density Waves.- 3.1. The Primary Idea of Lin and Shu of the Stationary Density Waves.- 3.2. The Spiral Galaxy as an Infinite System of Harmonic Oscillators.- 3.3. On “Two-Armness” of the Spiral Structure.- 3.4. The Main Difficulties of the Stationary Wave Theory of Lin and Shu.- §4. Linear Theory of Growing Density Waves.- 4.1. Spiral Structure as the Most Unstable Mode.- 4.2. Gravitational Instability at the Periphery of Galaxies.- 4.3. Waves of Negative Energy Generated Near the Corotation Circle and Absorbed at the Inner Lindblad Resonance—Lynden-BellKalnaj’s Picture of Spiral Pattern Maintenance.- 4.4. Kelvin–Helmholz Instability and Flute-like Instability in the Near-Nucleus Region of the Galaxy as Possible Generators of Spiral Structure.- 4.5. The “Trailing” Character of Spiral Arms.- § 5. Comparison of the Lin–Shu Theory with Observations.- 5. 1 The Galaxy.- 5.2. M33, M51, M81.- § 6. Experimental Simulation of Spiral Structure Generation.- 6. 1 In a Rotating Laboratory Plasma.- 6.2. In Numerical Experiment.- § 7. The Hypothesis of the Origin of Spirals in the SB-Galaxies.- XII Other Applications.- § 1 On the Structure of Saturn’s Rings.- l.1. Introduction.- 1.2. Model. Basic Equations.- 1.3. Jeans Instability.- 1.4. Dissipative Instabilities.- 1.5. Modulational Instability.- Appendix. Derivation of the Expression for the Perturbation Energy of Maclaurin’s Ellipsoid.- § 2. On the Law of Planetary Distances.- §3. Galactic Plane Bending.- 3.1. Quasistationary Tidal Deformation.- 3.2. Free Modes of Oscillations.- 3.3. Close Passage.- § 4. Instabilities in Collisions of Elementary Particles.- § 1. Collisionless Kinetic Equation and Poisson Equation in Different Coordinate Systems.- § 2. Separation of Angular Variables in the Problem of Small Perturbations of Spherically Symmetrical Collisionless Systems.- § 3. Statistical Simulation of Stellar Systems.- 3.1. Simulation of Stellar Spheres of the First Camm Series.- 3.2. Simulation of Homogeneous Nonrotating Ellipsoids.- § 4. The Matrix Formulation of the Problem of Eigenoscillations of a Spherically-Symmetrical Collisionless System.- § 5. The Matrix Formulation of the Problem of Eigenoscillations of Collisionless Disk Systems.- 5.1. The Main Ideas of the Derivation of the Matrix Equation.- 5.2. “Lagrange” Derivation of the Matrix Equation.- § 6. Derivation of the Dispersion Equation for Perturbations of the Three-Axial Freeman Ellipsoid.- § 7. WKB Solutions of the Poisson Equation Taking into Account the Preexponential Terms and Solution of the Kinetic Equation in the Postepicyclic Approximation.- 7.1. The Relation Between the Potential and the Surface Density.- 7.2. Calculations of the Response of a Stellar Disk to an Imposed Perturbation of the Potential.- § 8. On the Derivation of the Nonlinear Dispersion Equation for Collisionless Disk.- § 9. Calculation of the Matrix Elements for the Three-Waves Interaction.- § 10. Derivation of the Formulas for the Boundaries of Wave Numbers Range Which May Take Part in a Decay.- §11. Derivation of the Kinetic Equation for Waves.- § 12. Table of Non-Jeans Instabilities (with a Short Summary).- References.- Additional References.

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Book SynopsisThis book is about supergravity, which combines the principles of general relativity and local gauge invariance with the idea of supersymmetries between bosonic and fermionic degrees of freedom. The authors give a thorough and pedagogical introduction to the subject suitable for beginning graduate or advanced undergraduate students in theoretical high energy physics or mathematical physics. Interested researchers working in these or related areas are also addressed. The level of the presentation assumes a working knowledge of general relativity and basic notions of differential geometry as well as some familiarity with global supersymmetry in relativistic field theories. Bypassing curved superspace and other more technical approaches, the book starts from the simple idea of supersymmetry as a local gauge symmetry and derives the mathematical and physical properties of supergravity in a direct and “minimalistic” way, using a combination of explicit computations and geometrical reasoning. Key topics include spinors in curved spacetime, pure supergravity with and without a cosmological constant, matter couplings in global and local supersymmetry, phenomenological and cosmological implications, extended supergravity, gauged supergravity and supergravity in higher spacetime dimensions.Table of ContentsIntroduction.- From Global to Local SUSY.- Gravity and spinors.- D=4 N=1 SUGRA.- Matter couplings in global SUSY.- Matter couplings in SUGRA.- SUGRA phenomenology.- Extended supergravities.- Gauged supergravity.- SUGRA in any dimension.

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