Quantum physics Books

Book SynopsisIn the present treatise progress in topological approach to Hall system physics is reported, including recent achievements in graphene. The homotopy methods of braid groups turn out to be of particular convenience in order to grasp peculiarity of 2D charged systems upon magnetic field resulting in Laughlin correlations. The real progress in understanding of structure and role of composite fermions in Hall system is provided. The crucial significance of carrier mobility apart from interaction in creation of the fractional quantum Hall effect (FQHE) is described and supported by recent graphene experiments. Recent progress in FQHE field including topological insulators and optical lattices was reviewed and commented in terms of braid group approach. The braid group methods are presented from more general point of view including proposition of pure braid group application.Table of ContentsIntroduction; Elements of Hall System Physics in 2D Spaces; Topological Methods of Describing Systems of Many Particles at Various Manifolds; Cyclotron Braids for Multi-Particle Charged 2D Systems in a Strong Magnetic Field; Recent Progress in FQHE Field; Summary; Comments and Supplements.

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Book SynopsisQuantum computing — the application of quantum mechanics to information — represents a fundamental break from classical information and promises to dramatically increase a computer's power. Many difficult problems, such as the factorization of large numbers, have so far resisted attack by classical computers yet are easily solved with quantum computers. If they become feasible, quantum computers will end standard practices such as RSA encryption.Most of the books or papers on quantum computing require (or assume) prior knowledge of certain areas such as linear algebra or quantum mechanics. The majority of the currently-available literature is hard to understand for the average computer enthusiast or interested layman. This text attempts to teach quantum computing from the ground up in an easily readable way, providing a comprehensive tutorial that includes all the necessary mathematics, computer science and physics.Table of ContentsIntroduction; Computer Science; Mathematics for Quantum Computing; Quantum Mechanics; Quantum Computing; Information Theory; Quantum Algorithms; Using Quantum Mechanical Devices and Recent Developments.

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Book SynopsisThis book contains exclusively invited contributions from collaborators of Maximilian Kreuzer, giving accounts of his scientific legacy and original articles from renowned theoretical physicists and mathematicians, including Victor Batyrev, Philip Candelas, Michael Douglas, Alexei Morozov, Joseph Polchinski, Peter van Nieuwenhuizen, and Peter West.Besides a collection of review and research articles from high-profile researchers in string theory and related fields of mathematics (in particular, algebraic geometry) which discuss recent progress in the exploration of string theory vacua and corresponding mathematical developments, this book contains a pedagogical account of the important work of Brandt, Dragon, and Kreuzer on classification of anomalies in gauge theories. This highly cited work, which is also quoted in the textbook of Steven Weinberg on quantum field theory, has not yet been presented in full detail except in private lecture notes by Norbert Dragon.Similarly, the software package PALP (Package for Analyzing Lattice Polytopes with applications to toric geometry), which has been incorporated in the SAGE (Software for Algebra and Geometry Experimentation) project, has not yet been documented in full detail. This book contains a user manual for a new thoroughly revised version of PALP.By including these two very useful original contributions, researchers in quantum field theory, string theory, and mathematics will find added value in a pedagogical presentation of the classification of quantum gauge field anomalies, and the accompanying comprehensive manual and tutorial for the powerful software package PALP.Table of ContentsGauge Field Theory, Anomalies, and Supersymmetry: BRST Symmetry and Cohomology (N Dragon and F Brandt); Aspects of Supersymmetric BRST Cohomology (F Brandt); Character Expansion for HOMFLY Polynomials: Integrability and Difference Equations (A Mironov, A Morozov and A Morozov); Bicategories in Field Theories - An Invitation (T Nikolaus and C Schweigert); The Compactification of IIB Supergravity on S5 Revisited (P van Nieuwenhuizen); String Theory and Algebraic Geometry: Max Kreuzer's Contributions to the Study of Calabi - Yau Manifolds (P Candelas); Calabi - Yau Three-Folds: Poincare Polynomials and Fractals (A Ashmore and Y-H He); Conifold Degenerations of Fano 3-Folds as Hypersurfaces in Toric Varieties (V Batyrev and M Kreuzer); Nonassociativity in String Theory (R Blumenhagen); Counting Points and Hilbert Series in String Theory (V Braun); Standard Models and Calabi - Yaus (R Donagi); The String Landscape and Low Energy Supersymmetry (M R Douglas); The Cardy - Cartan Modular Invariant (J Fuchs, C Schweigert and C Stigner); A Projection to the Pure Spinor Space (S Guttenberg); Mathieu Moonshine and Symmetries of K3 Sigma Models (S Hohenegger); Toric Deligne - Mumford Stacks and the Better Behaved Version of the GKZ Hypergeometric System (R P Horja); Fano Polytopes (A M Kasprzyk and B Nill); Dual Purpose Landscaping Tools: Small Extra Dimensions in AdS/CFT (J Polchinski and E Silverstein); Notes on the Relation Between Strings, Integrable Models and Gauge Theories (R C Rashkov); E11, Generalised Space-Time and IIA String Theory: The R ⊗ R Sector (A Rocen and P West); The Kreuzer Bi-Homomorphism (A N Schellekens); Emergent Spacetime and Black Hole Probes from Automorphic Forms (R Schimmrigk); How to Classify Reflexive Gorenstein Cones (H Skarke); PALP - A Package for Analyzing Lattice Polytopes: PALP - A User Manual (A P Braun, J Knapp, E Scheidegger, H Skarke and N-O Walliser).

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Book SynopsisThis book provides a comprehensive account of basic concepts of quantum mechanics in a coherent manner. The book is self-contained and not only covers basic concepts in quantum mechanics but also provides a basis for applications in atomic and laser physics, nuclear and particle physics, and condensed matter physics. It also covers relativistic quantum mechanics, in particular the Dirac equation and its applications.Table of ContentsBreakdown of Classical Concepts; Quantum Mechanical Concepts; Basic Postulates of Quantum Mechanics; Solution of Problems in Quantum Mechanics; Simple Harmonic Oscillator; Angular Momentum; Motion in Centrally Symmetric Field; Collision Theory; Operators; Heisenberg Equation of Motion, Invariance Principle and Path Integral; Angular Momentum and Spin; Time Independent Perturbation Theory; Time Dependent Perturbation Theory; Statistics and the Exclusion Principle; Two State Systems; Quantum Computation; Perturbation Induced by Electromagnetic Field; Formal Theory of Scattering; S-Matrix and Invariance Principles; Relativistic Quantum Mechanics: Dirac Equation; Dirac Equation in (1+2) Dimensions: Application to Graphene.

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Book SynopsisQuantum cosmology has gradually emerged as the focus of devoted research, mostly within the second half of last century. As we entered the 21st century, the subject is still very much alive. The outcome of results and templates for investigation have been enlarged, some very recent and fascinating. Hence this book, where the authors bequeath some of their views, as they believe this current century is the one where quantum cosmology will be fully accomplished.Though some aspects are not discussed (namely, supersymmetry or loop structures), there are perhaps a set of challenges that in the authors' opinion remain, some since the dawn of quantum mechanics and applications to cosmology. Others could have been selected, at the readers' discretion and opinion. The authors put herewith a chart and directions to explore, some of which they have worked on or aimed to work more, in the twilight of their current efforts. Their confidence is that someone will follow in their trails, venturing in discovering the proper answer, by being able to formulate the right questions beforehand. The authors' shared foresight is that such discoveries, from those formulations, will be attained upon endorsing the routes within the challenges herewith indicated.Table of ContentsStanding Point: Introduction Point; A Reader's Digest; Routes: Degeneracy of Solutions; Landscape and Selection Rules; Singularity Avoidance; Observational Issues; Wheeler - deWitt Equation and Hilbert Space Structure; Chaos and Integrability; Elements from Strings and Loops; Other Routes; Appendices: Hamiltonian Formulation; Superspace Quantization; Semi-Classical Gravity; Minisuperspace; Boundary Conditions; 'Predictions' from Quantum Cosmology.

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Book SynopsisThese pages offer a simple, analytic, functional approach to non-perturbative QFT, using a frequently overlooked functional representation of Fradkin to explicitly calculate relevant portions of the Schwinger Generating Functional (GF). In QED, this corresponds to summing all Feynman graphs representing virtual photon exchange between charged particles. It is then possible to see, analytically, the cancellation of an infinite number of perturbative, UV logarithmic divergences, leading to an approximate but most reasonable statement of finite charge renormalization.A similar treatment of QCD, with the addition of a long-overlooked but simple rearrangement of the Schwinger GF which displays Manifest Gauge Invariance, is then able to produce a simple, analytic derivation of quark-binding potentials without any approximation of infinite quark masses. A crucial improvement of previous QCD theory takes into account the experimental fact that asymptotic quarks are always found in bound states; and therefore that their transverse coordinates can never be measured, nor specified, exactly. And this change of formalism permits a clear and simple realization of true quark binding, into mesons and nucleons. An extension into the QCD binding of two nucleons into an effective deuteron presents a simple, analytic derivation of nuclear forces.Finally, a new QED-based solution of Vacuum Energy is displayed as a possible candidate for Dark Energy. An obvious generalization to include Inflation, which automatically suggests a model for Dark Matter, is immediately possible; and one more obvious generalization produces an understanding of the origin of the Big Bang, and of the Birth (and Death) of a Universe. If nothing else, this illustrates the Power and the Reach of Quantum Field Theory.Table of ContentsFunctional Preliminaries: QFT - Why and How; Functional Field Theory; Generating Functional and the S-Matrix; Schwinger - Fradkin Representations; Perturbative Radiative Corrections to the Photon Propagator; Finite, Non-perturbative Charge Renormalization; Radiative Corrections to the Fermion Propagator; Ideal and Realistic QCD; A New, Analytic, Non-perturbative, Gauge-invariant Formulation; Effective Locality; Analytic Quark Binding; Analytic Nucleon Binding; New QED Symmetry-Breaking Model of Vacuum Energy, with application to Inflation and Dark Energy; Astrophysical Implications of Tachyon Pairs in the Quantum Vacuum: Supernova and the Schwinger Mechanism; Dark Matter; Gamma-Ray Bursts; Ultra High-Energy Cosmic Rays; Loop Annihilation and Fermi Bubbles; Final Speculations.

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Book SynopsisThis book contains advanced subjects in solid state physics with emphasis on the theoretical exposition of various physical phenomena in solids using quantum theory, hence entitled “A modern course in the quantum theory of solids”. The use of the adjective “modern” in the title is to reflect the fact that some of the new developments in condensed matter physics have been included in the book. The new developments contained in the book are mainly in experimental methods (inelastic neutron scattering and photoemission spectroscopy), in magnetic properties of solids (the itinerant magnetism, the superexchange, the Hubbard model, and giant and colossal magnetoresistance), and in optical properties of solids (Raman scattering). Besides the new developments, the Green's function method used in many-body physics and the strong-coupling theory of superconductivity are also expounded in great detail.Table of ContentsLattice Dynamics; Determination of Phonon Dispersion Relations; Elementary Theory of Energy Bands; Determination of Electronic band Structures; Electron - Phonon Interaction; Transport Properties of Solids; Magnetic Properties of Solids; Optical Properties of Solids; Superconductivity.

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Book SynopsisThis book is a collection of lecture notes from the Symposium on Quantum Computing, Thermodynamics, and Statistical Physics, held at Kinki University in March 2012. Quantum information theory has a deep connection with statistical physics and thermodynamics. This volume introduces some of the topics on interface among the mentioned fields. Subjects included in the lecture notes include quantum annealing method, nonequilibrium thermodynamics and spin glass theory, among others. These subjects were presented with much emphasis put in its relevance in quantum information theory. These lecture notes are prepared in a self-contained manner so that a reader with modest background may understand the subjects.

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Book SynopsisThis book is a collection of contributions to the Symposium on Interface between Quantum Information and Statistical Physics held at Kinki University in November 2011. Subjects of the symposium include quantum adiabatic computing, quantum simulator using bosons, classical statistical physics, among others. Contributions to this book are prepared in a self-contained manner so that a reader with a modest background may understand the subjects.Table of ContentsBosons in an Optical Lattice with a Synthetic Magnetic Field (K Kasamatsu); Quantum Simulation Using Exciton-Polaritons and Their Applications Toward Accelerated Optimization Problem Search (T Byrnes, K Yan, K Kusudo, M Fraser and Y Yamamoto); Quantum Simulation Using Ultracold Atoms in Optical Lattices (S Sugawa, S Taie, R Yamazaki, and Y Takahashi); Universality of Integrable Model: Baxter's T-Q Equation, SU(N)/SU(2)N-3 Correspondence and Ω-Deformed Seiberg-Witten Prepotential (Ta-sheng Tai); Exact Analysis of Correlation Functions of the XXZ Chain (T Deguchi, K Motegi and J Sato); Classical Analogue of Weak Value in Stochastic Process (H Tomita); Scaling of Entanglement Entropy and Hyperbolic Geometry (H Matsueda); From Classical Neural Networks to Quantum Neural Networks (B Tirozzi); Analysis of Quantum Monte Carlo Dynamics in Infinite-range Ising Spin Systems: Theory and Its Possible Applications (J Inoue); A Method to Control Order of Phase Transition: Invisible States in Discrete Spin Models (R Tamura, S Tanaka and N Kawashima); Quantum Annealing and Quantum Fluctuation Effect in Frustrated Ising Systems (S Tanaka and R Tamura).

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Book SynopsisBlack holes, once just fascinating theoretical predictions of how gravity warps space-time according to Einstein's theory, are now generally accepted as astrophysical realities, formed by post-supernova collapse, or as supermassive black holes mysteriously found at the cores of most galaxies, powering active galactic nuclei, the most powerful objects in the universe. Theoretical understanding has progressed in recent decades with a wider realization that local concepts should characterize black holes, rather than the global concepts found in textbooks. In particular, notions such as trapping horizon allow physically meaningful quantities and equations, describing how a black hole evolves. This has led to discoveries in fields as diverse as classical and numerical general relativity, differential geometry, thermodynamics, quantum field theory, and quantum gravity. There is heretofore no one volume which covers all the main aspects, so this volume collects together summaries and recent research, each chapter written by an expert or experts in a given field. This is intended for readers at a graduate level upwards, who wish to learn about the wide range of research concerning black holes.Table of ContentsAn Introduction to Local Black Hole Horizons in the 3+1 Approach to General Relativity (Jose Luis Jaramillo); Physical Aspects of Quasi-Local Black Hole Horizons (Alex B Nielsen); On Uniqueness Results for Static, Asymptotically Flat Initial Data Containing MOTS (Alberto Carrasco and Marc Mars); Horizons in the Near-Equilibrium Regime (Ivan Booth); Isolated Horizons in Classical and Quantum Gravity (Jonathan Engle and Tomas Liko); Quantum Thermometers in Stationary Space-Times with Horizons (Sergio Zerbini); Relativistic Thermodynamics (Sean A Hayward); Trapped Surfaces (J M M Senovilla); Some Examples of Trapped Surfaces (I Bengtsson).

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Book SynopsisThis book is a collection of lecture notes and contributions in “Summer School on Diversities in Quantum Computation/Information” held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relativistic quantum information, quantum computing of link polynomials, quantum algorithms, etc. Each lecture note is written in a self-contained manner so that it may be used as a textbook for one semester graduate course or advanced undergraduate course. Contributions report current research subjects also in a self-contained manner. We believe that these articles are accessible to the readers form various disciplines.Table of ContentsMatrix Techniques in Quantum Information Science (C-K Li); Untying Knots by NMR: Experimental Implementation of an Exponentially Fast Quantum Algorithm for Approximating the Jones Polynomial (R Marx); Quantum Algorithms for Algebraic Problems (W van Dam); Lecture Series on Relativistic Quantum Information (I Fuentes); Systematic Construction of Bell-Like Inequalities and Proposal of a New Type of Test (S Tanimura); Hybrid Quantum Annealing for Clustering Problems (S Tanaka, R Tamura, I Sato & K Kurihara); Theory of Macroscopic Quantum Tunneling in Two-Gap Superconductors: Corrections from Leggett's Modes (Y Ota, M Machida & T Koyama).

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Book SynopsisThis book is a broad-based text intended to help the growing student body interested in constructing and applying methods of effective field theory to solve problems in their research. It begins with a review of using symmetries to identify the relevant degrees of freedom in a problem, and then presents a variety of methods that can be used to construct various effective theories. A detailed discussion of canonical applications of effective field theory techniques with increasing complexity is given, including Fermi's weak interaction, heavy-quark effective theory, and soft-collinear effective theory. Applications of these techniques to study physics beyond the standard model, dark matter, and quantum and classical gravity are explored. Although most examples come from questions in high-energy physics, many of the methods can also be applied in condensed-matter settings. Appendices include various factoids from group theory and other topics that are used throughout the text, in an attempt to make the book self-contained.Table of ContentsSymmetries; Elementary Techniques; Effective Field Theories of Type-I; Effective Field Theories of Type-II; Effective Field Theories of Type-III; Supersymmetric Effective Field Theories; Effective Field Theories on the Lattice; Effective Field Theories of Gravity; Outlook.

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Book SynopsisYang-Mills gravity is a new theory, consistent with experiments, that brings gravity back to the arena of gauge field theory and quantum mechanics in flat space-time. It provides solutions to long-standing difficulties in physics, such as the incompatibility between Einstein's principle of general coordinate invariance and modern schemes for a quantum mechanical description of nature, and Noether's ‘Theorem II’ which showed that the principle of general coordinate invariance in general relativity leads to the failure of the law of conservation of energy. Yang-Mills gravity in flat space-time appears to be more physically coherent than conventional gravity in curved space-time. The problems of quantization of the gravitational field, the operational meaning of space-time coordinates and momenta, and the conservation of energy-momentum are all resolved in Yang-Mills gravity.The aim of this book is to provide a treatment of quantum Yang-Mills gravity, with an emphasis on the ideas and evidence that the gravitational field is the manifestation of space-time translational symmetry in flat space-time, and that there exists a fundamental space-time symmetry framework that can encompass all of physics, including gravity, for all inertial and non-inertial frames of reference.Table of ContentsTaiji Symmetry Framework for all Physics in Inertial and Non-Inertial Frames of Reference: Space-Time Symmetry, Natural Units and Fundamental Constants; Taiji Relativity Based Solely on the Principle of Relativity; Limiting Continuation of Space-Time Transformations and Accelerated Wu Transformations; General Linear-Acceleration Transformations and Taiji Pseudo-Group; Rotational Space-Time Transformations and Rotational Pseudo-Group; Taiji Symmetry Framework and Symmetric Energy-Momentum Tensors; Yang - Mills Gravity and its Unification with Other Interactions Based on Taiji Symmetry Framework: Yang - Mills - Utiyama - Weyl Framework for Internal and External Gauge Symmetries; Yang - Mills Gravity Based on Taiji Space-Time and Effective Metric Tensors for Planets' Motion; Experimental Consistency of Yang - Mills Gravity; Quantization of Yang - Mills Gravity and Feynman Rules; The S-Matrix of Yang - Mills Gravity, Gauge Invariance and Unitarity; Gravitational Self-Energies of the Gravition; Space-Time Gauge Identities and Finite-Loop Renormalization for Gravity; The Unified Gravity-Electroweak Model Within Yang - Mills - Utiyama - Weyl Framework; A Unified Model of Quantum Chromodynamics and Yang - Mills Gravity; Outlook.

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Book SynopsisThis is a collection of articles on fundamental physical principles and methods, the topics ranging from matrix models, random surfaces, quantum dots and rings, to black holes, cosmology and testing of the tiny effects predicted by General Relativity. Among the authors are Sir Roger Penrose and other well-known experts and the articles are addressed to graduate students and researchers. The volume is a Festschrift to a noted physicist and mentor Sergei Matinyan.Table of ContentsA Matrix Model Representation of the Integrable XXZ Heisenberg Chain on Random Surfaces (J Ambjorn and A Sedrakyan); Magnetization and Concurrence Properties of Diamond Chain: Two Approaches (N S Ananikian, H A Lazaryan, M A Nalbandyan and O Rozas an de Souza); Non-Trivial Holonomy and Calorons (P van Baal); On Emergent Gauge and Gravity Theories (J L Chkareuli); Collective States of D(D3) Non-Abelian Anyons (P E Finch and H Frahm); Electromagnetic Properties of Neutrinos at an Interface (A N Ioannisian, D A Ioannisian and N A Kazarian); Capture and Ejection of Dark Matter by the Solar System (I B Khriplovich); Topological Theory Of QHE (M Kohmoto); QCD String as an Effective String (Y Makeenko); New Chern - Simons Densities in Both Odd and Even Dimensions (E Radu and T Tchrakian); Constraints on Parameters of the Black Hole at the Galactic Center (A F Zakharov, F De Paolis, G Ingrosso and A A Nucita); Diffusion in Two-Dimensional Disordered Systems with Particle-Hole Symmetry (K Ziegler); and other papers.

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Book SynopsisQuantum Chromodynamics (QCD) is the most up-to-date theory of the strong interaction. Its predictions have been verified experimentally, and it is a cornerstone of the Standard Model of particle physics. However, standard perturbative procedures fail if applied to low-energy QCD. Even the discovery of the Higgs Boson will not solve the problem of masses originating from the non-perturbative behavior of QCD.This book presents a new method, the introduction of the ‘mass gap’, first suggested by Arthur Jaffe and Edward Witten at the turn of the millennium. It attempts to show that, to explain the mass-spectrum of QCD, one needs the mass scale parameter (the mass gap) instead of other massive particles. The energy difference between the lowest order and the vacuum state in Yang-Mills quantum field theory, the mass gap is in principle responsible for the large-scale structure of the QCD ground state, and thus also for its non-perturbative phenomena at low energies. This book not only presents the mass gap, but also details the applications and outlook of the mass gap method. A detailed summary of references and problems are included as well.This book is best for scientists and highly advanced students interested in non-perturbative effects and methods in QCD.Table of ContentsTheory of the Mass Gap: Quantum Chromodynamics and the Mass Gap; Color Gauge Invariance and the Origin of the Mass Gap; Formal Exact Solutions for the Full Gluon Propagator at Non-zero Mass Gap; Renormalization of the Mass Gap; General Discussion; Applications of the Mass Gap: Vacuum Energy Density in the Quantum Yang - Mills Theory; The Non-perturbative Analytical Equation of State for the Gluon Matter I; The Non-perturbative Analytical Equation of State for the Gluon Matter II; The Non-perturbative Analytical Equation of State for SU(3) Gluon Plasma.

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Book SynopsisThis volume is based on the fifth international conference of quantum bio-informatics held at the QBI Center of Tokyo University of Science.This volume provides a platform to connect mathematics, physics, information and life sciences, and in particular, research for new paradigm for information science and life science on the basis of quantum theory.The following topics are discussed:Table of ContentsComplexity Considerations Quantum Computation (Luigi Accardi); Oscillations and Rolling for Duffing's Equation (Irina Ya Aref'eva, Evgeny V Piskovskiy and Igor V Volovich); A Mathematical Treatment of Joint and Conditional Probability (Masanori Asano, Masanori Ohya, Yoshiharu Tanaka, Ichiro Yamato, Irina Besieva and Andrei Khrennikov); Minimum of Information Distance Criterion for Optimal Control of Mutation Rate in Evolutionary Systems (Roman V Belavkin); On Non-Markovian Quantum Evolution (Dariusz Chruscinski and Andrzej Kossakowski); Internal Noise of EEG-Measurements and Certain Boson Systems (Karl-Heinz Fichtner, Lars Fichtner, Kei Inoue and Masanori Ohya); Space - Time - Noise (Raum - Zeit - Rauschen) (Takeyuki Hida); A New Noise Depending on a Space Parameter and Its Application (Si Si and Win Win Htay); Schrodinger Type Semigroups via Feynman Formulae and All That (Oleg G Smolyanov); On Treatment of Gaussian Communication Process by Quantum Entropies (Noboru Watanabe); Signaling Networks Involving Reactive Oxygen Species and Ca2+ in Plants (Kazuyuki Kuchitsu); Energy Flow and Information Flow in Superconducting Qubit Measurement Process (Hayato Nakano); Counter-factual Phenomenon in Quantum Mechanics (Yutaka Shikano); and other papers.

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Book SynopsisBased on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory.This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.Table of ContentsGeneralized Euler Characteristics, Graph Hypersurfaces and Feynman Periods; Noncommutative Spacetimes and Quantum Physics; Index Theory of Non-Compact G-Manifolds; Compactifications of String Theory and Generalized Geometry; Spectral Geometry; Noncommutative Geometry Models for Particle Physics; Integrability and the AdS/CFT Correspondence; Introductory Lectures on Chern - Simons Theories in Physics; Grothendieck Ring Class of Banana and Flower Graphs; Groupoids and Poisson Sigma Models with Boundary; On the Geometry Underlying a Real Lie Algebra Representation; A Survey on Orbifold String Topology.

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Book SynopsisThis volume is based on lectures given during the program “Complex Quantum Systems” held at the National University of Singapore's Institute for Mathematical Sciences from 17 February to 27 March 2010. It guides the reader through two introductory expositions on large Coulomb systems to five of the most important developments in the field: derivation of mean field equations, derivation of effective Hamiltonians, alternative high precision methods in quantum chemistry, modern many-body methods originating from quantum information, and — the most complex — semirelativistic quantum electrodynamics.These introductions are written by leaders in their fields; amongst them are Volker Bach, Rafael Benguria, Thomas Chen, and Jan Philip Solovej. Together, they fill a gap between current textbooks and the vast modern literature on complex quantum systems.Table of ContentsStability of Matter (Rafael Benguria and Benjamin Loewe); Mathematical Density and Density Matrix Functional Theory (Volker Bach); On the Dynamics of a Fermi Gas in a Random Medium with Dynamical Hartree - Fock Interactions (Thomas Chen); On the Minimization of Hamiltonians over Pure Gaussian States (Jan Derezinski, Marcin Napiorkowski and Jan Philip Solovej); Variational Approach to Electronic Structure Calculations on Second-Order Reduced Density Matrices and the N-Representability Problem (Maho Nakata, Mituhiro Fukuda, and Katsuki Fujisawa); Fermionic Many-Body Systems: A Quantum Information Approach (Christina Kraus); Hydrogen-Like Atoms in Relativistic QED (Martin Konenberg, Oliver Matte and Edgardo Stockmeyer).

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Book Synopsis'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.Table of ContentsVolume 1: Classical Relativistic Field Theory: Kinematical Aspects; Classical Relativistic Field Theory: Dynamical Aspects; Relativistic Quantum Field Theory: Operator Methods; Nonrelativistic Quantum Mechanics: Functional Methods; Relativistic Quantum Field Theory: Functional Integral Methods; Quantum Field Theory at Nonzero Temperature; Volume 2: Symmetries and Canonical Formalism; Gauge Symmetries and Constrained Systems; Weyl Quantization; Anomalies in Quantum Field Theory; Noncommutative Geometry; Quantum Groups; Noncommutative Geometry and Quantum Groups.

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Book SynopsisDimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that “something else” is needed to quickly gain insight into the system they are going to study. Qualitative methods are this “something else”, but typically, students have never heard of them before.The aim of this book is to teach the craft of qualitative analysis using a set of problems, some with solutions and some without, in advanced undergraduate and beginning graduate Quantum Mechanics. Examples include a dimensional analysis solution for the spectrum of a quartic oscillator, simple WKB formulas for the matrix elements of a coordinate in a gravitational well, and a three-line-long estimate for the ionization energy of atoms uniformly valid across the whole periodic table. The pièce de résistance in the collection is a series of dimensional analysis questions in Integrable Nonlinear Partial Differential Equations with no dimensions existing a priori. Solved problems include the relationship between the size and the speed of solitons of the Korteweg-de Vries equation and an expression for the oscillation period of a Nonlinear Schrödinger breather as a function of its width.Table of ContentsWKB Approximation; "Halved" Harmonic Oscillator: A Case Study; Perturbation Theory; Variational Problems; Gravitational Well: A Case Study; Some Exotic Exactly Solvable Problems; Mean-Field Theories; Integrable Nonlinear Partial Differential Equations.

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Book SynopsisThis is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions — density matrices in a special Weyl representation — and star products are the cornerstones of the formalism.The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject.In this logically complete and self-standing formulation, one need not choose sides between coordinate or momentum space variables. It works in full phase space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory. The observables in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, only composed together in novel algebraic ways using star products.This treatise provides an introductory overview and supplementary material suitable for an advanced undergraduate or a beginning graduate course in quantum mechanics.Table of ContentsHistorical Survey; The Veridical Paradox; So fasst uns das, was wir nicht fassen konnten, voller Erscheinung - [Rilke]; A Stay Against Confusion; Dirac; Groenewold; Moyal; Introduction; The Wigner Function; Solving for the Wigner Function; The Uncertainty Principle; Ehrenfest's Theorem; Illustration: The Harmonic Oscillator; Time Evolution; Nondiagonal Wigner Functions; Stationary Perturbation Theory; Propagators and Canonical Transformations; The Weyl Correspondence; Alternate Rules of Association; The Groenewold van Hove Theorem and the Uniqueness of MB and *-Products; Advanced Topic: Quasi-Hermitian Quantum Systems; Omitted Miscellany; Synopses of Selected Papers.

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Book SynopsisThe functional formulation of quantum mechanics and relativistic quantum field theories are widely studied subjects. Nevertheless, certain aspects of this formulation are frequently overlooked, in spite of their relevance from a structural point of view. This book aims to fill up this gap. The non-relativistic regime has been found particularly appropriate for these purposes.

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Book SynopsisQuantum physics has, on the one hand, drastically changed our theoretical description of the physical world and has, on the other hand, revolutionized everyday life, by allowing us to build lasers, atomic clocks used in GPS, and semiconductor-based devices such as laptop computers and smartphones. The object of this book is to give a self-contained introduction to both aspects. It contains a detailed account of the foundational principles: superposition, entanglement, quantum non-locality, decoherence and measurement theory, and of some selected applications: quantum cryptography and quantum computers, cold atoms, light emitting and laser diodes, and atomic clocks. The book is aimed at a general audience and the only prerequisite is a high-school background in mathematics.Table of ContentsAn Inconvenient Principle; Secure Communications; Einstein, Bohr, and Bell; Atoms, Light, and Lasers; Cold Atoms; The Kingdom of Semiconductors; Relativistic Quantum Physics; Towards a Quantum Computer; The Environment is Watching; Interpretations.

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Book SynopsisIn this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined.In addition, by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved.Table of ContentsA Brief History of Quantum Tunneling; Some Basic Questions Concerning Quantum Tunneling; Simple Solvable Problems; Time-Dependence of the Wave Function in One-Dimensional Tunneling; Semiclassical Approximations; Generalization of the Bohr - Sommerfeld Quantization Rule and its Application to Quantum Tunneling; Gamow's Theory, Complex Eigenvalues, and the Wave Function of a Decaying State; Tunneling in Symmetric and Asymmetric Local Potentials and Tunneling in Nonlocal and Quasi-Solvable Barriers; Classical Descriptions of Tunneling; Tunneling in Time-Dependent Barriers; Decay Width and Scattering Theory; The Method of Variable Reflection Amplitude Applied to Solve Multichannel Tunneling Problems; Path Integral and Its Semi-Classical Approximation in Quantum Tunneling; Heisenberg's Equations of Motion for Tunneling; Wigner Distribution Function in Quantum Tunneling; Decay Widths of Siegert States, Complex Scaling and Dilatation Transformation; Multidimensional Quantum Tunneling; Group and Signal Velocities; Time-Delay, Reflection Time Operator and Minimum Tunneling Time; More about Tunneling Time; Tunneling of a System with Internal Degrees of Freedom; Motion of a Particle in a Waveguide with Variable Cross Section and in a Space Bounded by a Dumbbell-Shaped Object; Relativistic Formulation of Quantum Tunneling; Inverse Problems of Quantum Tunneling; Some Examples of Quantum Tunneling in Atomic and Molecular Physics; Some Examples from Condensed Matter Physics; Alpha Decay.

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Book SynopsisThis is the solution manual for Riazuddin's and Fayyazuddin's Quantum Mechanics (2nd edition). The questions in the original book were selected with a view to illustrate the physical concepts and use of mathematical techniques which show their universality in tackling various problems of different physical origins. This solution manual contains the text and complete solution of every problem in the original book. This book will be a useful reference for students looking to master the concepts introduced in Quantum Mechanics (2nd edition).Table of ContentsBreakdown of Classical Concepts; Quantum Mechanical Concepts; Basic Postulates of Quantum Mechanics; Solution of Problems in Quantum Mechanics; Simple Harmonic Oscillator; Angular Momentum; Motion in Centrally Symmetric Field; Collision Theory; Operators; Heisenberg Equation of Motion, Invariance Principle and Path Integral; Angular Momentum and Spin; Time Independent Perturbation Theory; Time Dependent Perturbation Theory; Statistics and the Exclusion Principle; Two State Systems; Quantum Computation; Perturbation Induced by Electromagnetic Field; Formal Theory of Scattering; S-Matrix and Invariance Principles; Relativistic Quantum Mechanics: Dirac Equation; Dirac Equation in (1+2) Dimensions: Application to Graphene.

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Book SynopsisThis book aims to present a pedagogical and self-consistent treatment of the canonical approach to Quantum Gravity, starting from its original formulation to the most recent developments in the field.We start with an innovative and enlightening introduction to the formalism and concepts on which General Relativity has been built, giving all the information necessary in the later analysis. A brief sketch of the Standard Cosmological Model describing the Universe evolution is also given alongside the analysis of the inflationary mechanism. After deepening the fundamental properties of constrained dynamic systems, the Lagrangian approach to the Einsteinian Theory is presented in some detail, underlining the parallelism with non-Abelian gauge theories. Then, the basic concepts of the canonical approach to Quantum Mechanics are provided, focusing on all those formulations which are relevant for the Canonical Quantum Gravity problem. The Hamiltonian formulation of General Relativity and its constrained structure is then analyzed by comparing different formulations. The resulting quantum dynamics, described by the Wheeler-DeWitt equation, is fully discussed in order to outline its merits and limits. Afterwards, the reformulation of Canonical Quantum Gravity in terms of the Ashtekar-Barbero-Immirzi variables is faced by a detailed discussion of the resulting Loop Quantum Gravity Theory. Finally, we provide a consistent picture of canonical Quantum Cosmology by facing the main features of the Wheeler-DeWitt equation for the homogeneous Bianchi models and then by a detailed treatment of Loop Quantum Cosmology, including very recent developments.Table of ContentsGeneral Relativity; Quantization Methods; Classical and Quantum Geometrodynamics; Gravity as a Gauge Theory; Loop Quantum Gravity; Quantum Cosmology.

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Book SynopsisIn this book, we introduce quantum computation and its application to AI. We highlight problem solving and knowledge representation framework. Based on information theory, we cover two main principles of quantum computation — Quantum Fourier transform and Grover search. Then, we indicate how these two principles can be applied to problem solving and finally present a general model of a quantum computer that is based on production systems.Table of ContentsComputation; Production Systems; Human Problem Solving; Information Theory; Markov Chains; Introduction to Quantum Physics; Computation with Qubits; Discrete Fourier Transform and Quantum Fourier Transform; Order Finding; Quantum Search; Grover's Algorithm and Householder Reflection; Quantum Tree Search; Quantum Problem Solving; General Model of Quantum Computer; Quantum Cognition.

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Book SynopsisStarting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions:Table of ContentsWhat are Quantum Fractals?; Cantor Set; Iterated Function Systems; Cantor System Through Matrix Eigenvector; Quantum Iterated Function Systems; The 'Impossible' Quantum Fractal; Lorentz Group; SL(2,C), and Relativistic Aberration; Hyperbolic Quantum Fractals; Platonic Quantum Fractals for a Qubit; Controlling Chaotic Behavior and Fractal Dimension; Quantum Fractals on N-Spheres; Clifford Algebras; Frobenius - Perron Operator; Computer Simulations; Foundational Questions; Stochastic Nature of Quantum Measurement Processes; Are There Quantum Jumps?; Bohmian Mechanics; Ghirardi - Rimini - Weber Spontaneous Localization; Event Enhanced Quantum Theory; Heisenberg's Uncertainty Principle and Quantum Fractals; Are Quantum Fractals Real?; Limits of Quantum Computation.

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Book SynopsisAlthough there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions to several chapters.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it can be used by senior undergraduates too.Table of ContentsMathematical Prerequisites; The Formulation of Quantum Mechanics; Kinematics and Dynamics; Coordinate Representation and Applications; Momentum Representation and Applications; The Harmonic Oscillator; Angular Momentum; State Preparation and Determination; Measurement and the Interpretation of States; Formation of Bound States; Charged Particle in a Magnetic Field; Time-Dependent Phenomena; Discrete Symmetries; The Classical Limit; Quantum Mechanics in Phase-Space; Scattering; Identical Particles; Many-Fermion Systems; Quantum Mechanics of the Electromagnetic Field; Bell's Theorem and Its Consequences; Quantum Information.

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Book SynopsisAlthough there are many textbooks that deal with the formal apparatus of quantum mechanics (QM) and its application to standard problems, none take into account the developments in the foundations of the subject which have taken place in the last few decades. There are specialized treatises on various aspects of the foundations of QM, but none that integrate those topics with the standard material. This book aims to remove that unfortunate dichotomy, which has divorced the practical aspects of the subject from the interpretation and broader implications of the theory.In this edition a new chapter on quantum information is added. As the topic is still in a state of rapid development, a comprehensive treatment is not feasible. The emphasis is on the fundamental principles and some key applications, including quantum cryptography, teleportation of states, and quantum computing. The impact of quantum information theory on the foundations of quantum mechanics is discussed. In addition, there are minor revisions to several chapters.The book is intended primarily as a graduate level textbook, but it will also be of interest to physicists and philosophers who study the foundations of QM. Parts of it can be used by senior undergraduates too.Table of ContentsMathematical Prerequisites; The Formulation of Quantum Mechanics; Kinematics and Dynamics; Coordinate Representation and Applications; Momentum Representation and Applications; The Harmonic Oscillator; Angular Momentum; State Preparation and Determination; Measurement and the Interpretation of States; Formation of Bound States; Charged Particle in a Magnetic Field; Time-Dependent Phenomena; Discrete Symmetries; The Classical Limit; Quantum Mechanics in Phase-Space; Scattering; Identical Particles; Many-Fermion Systems; Quantum Mechanics of the Electromagnetic Field; Bell's Theorem and Its Consequences; Quantum Information.

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Book SynopsisThis book of essays in four parts, was written over a decade and full of surprises for the breadth and variety of its subject matter. The first part is about the foundations of the quantum theory which reflects the author's many conversations with the late John Bell who persuaded him that there is still no satisfactory interpretation of the theory. The second part deals with nuclear weapons. One of the essays concerns the creation of the modern gas centrifuge which was done by German prisoners of war in the Soviet Union. The proliferation of these centrifuges was one of the issues in the spread of nuclear weapons. The third section deals with financial engineering with a profile of Louis Bachelier, the French mathematician who created it at the beginning of the 20th century. The final section deals with the Higgs boson and how it is used for generating mass. It includes a detailed article of how this mechanism works.

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Book SynopsisThis book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics.Table of ContentsBasic Principles; Quantum Fields; Quantum Fields in Riemann Spacetime; Symmetry Breaking; Perturbative Field Theory; From Quantum Field Theory to Quantum Mechanics; Electromagnetic Field; Quantum Mechanics; Applications of Quantum Mechanics; Statistical Mechanics; Applications of Statistical Mechanics; General Relativity; Tensors; Functional Formula; Gaussian Integrals; Grassmann Algebra; Euclidean Representation; Some Useful Formulas; Jacobian; Geodesic Equation.

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Book SynopsisThis book presents a brief introduction to the quantum field theory of the Standard Model for quarks and leptons. With minimal use of mathematics, it covers the basics of quantum field theory, local gauge field theory, spontaneous symmetry breaking mechanism, the Higgs mechanism and quantum chromodynamics.From the time when the first edition was published until today, the field of particle physics has seen some major break-through with the possible discovery of Higgs particle, also known as the Higgs boson. In the second edition, the famous Higgs mechanism is included to explain the symmetry breaking in the Standard Model and the origin of mass, and all of this is explained in high-school level algebra.Aimed at both scientists and non-specialists, it requires only some rudimentary knowledge of the Lagrangian and Hamiltonian formulation of Newtonian mechanics as well as a basic understanding of the special theory of relativity and quantum mechanics to enjoy this book.Table of ContentsParticles and Fields I: Dichotomy; Lagrangian and Hamiltonian Dynamics; Canonical Quantization; Particles and Fields II: Duality; Equations for Duality; Electromagnetic Field; Emulation of Light I: Matter Fields; Road Map for Field Quantization; Particles and Fields III: Particles as Quanta of Fields; Emulation of Light II: Interactions; Triumph and Wane; Leptons and Quarks; What is Gauge Field Theory?; The Weak Gauge Fields; The Higgs Mechanism and the Electroweak Gauge Fields; The Higgs Particle; Evolution of the Strong Force; The History of Color SU(3) Symmetry; Quantum Chromodynamics, QCD; Appendices: The Natural Unit System; Notation; Velocity-Dependent Potential; Fourier Decomposition of Field; Mass Units for Particles; Mass-Range Relation.

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Book SynopsisThis book provides a new original perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, in spite of its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted interpretation. The novelty of the book comes from the multiple viewpoints and the original angles taken by a group of young researchers from Europe and South America who gathered for several years under the auspices of the Center Leo Apostel.Each member of the group presented ideas concerning the interpretation of quantum mechanics. We had discussions ranging from the philosophical underpinnings of local realism and holism, information and decision theoretic approaches to quantum theory all the way to the many worlds interpretation. Strikingly, in much the same way as different — and indeed incompatible observations are needed to fully describe the physical state of affairs in quantum mechanics — the various interpretations of the theory also seem to shed viable, but not necessarily compatible, perspectives on different aspects of the same grand framework. The discussions that followed were both technical and lively, but perhaps their most remarkable quality was the absence of rigid points of view that unfortunately seems to paralyze so much of the discussion in this area. This book is an expression which can be interesting not only to the specialists but also for the general public attempting to get a grasp on one of the still most fundamental questions of present physics.

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Book SynopsisThis book is a collection of contributions from a Summer Workshop on “Physics, Mathematics, and All That Quantum Jazz”. Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects.

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Book SynopsisThis book is a sequel to the volume of selected papers of Dyson up to 1990 that was published by the American Mathematical Society in 1996. The present edition comprises a collection of the most interesting writings of Freeman Dyson, all personally selected by the author, from the period 1990-2014.The five sections start off with an Introduction, followed by Talks about Science, Memoirs, Politics and History, and some Technical Papers. The most noteworthy is a lecture entitled Birds and Frogs to the American Mathematical Society that describes two kinds of mathematicians with examples from real life. Other invaluable contributions include an important tribute to C. N. Yang written for his retirement banquet at Stony Brook University, as well as a historical account of the Operational Research at RAF Bomber Command in World War II provocatively titled A Failure of Intelligence. The final section carries the open-ended question of whether any conceivable experiment could detect single gravitons to provide direct evidence of the quantization of gravity — Is a Graviton Detectable? Various possible graviton-detectors are examined.This invaluable compilation contains unpublished lectures, and surveys many topics in science, mathematics, history and politics, in which Freeman Dyson has been so active and well respected around the world.

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Book SynopsisThis book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to Classical Mechanics connects different fields like Hamiltonian mechanics and differential geometry, so the book is suitable for students and researchers from various disciplines.Table of ContentsQuantum Mechanics and Summing Up Amplitudes; Double Slit Experiment; Infinite Slits Experiments and Path-Correspondence; Dirac's 1932 Paper on Small Time Amplitudes; Time-Slicing: From Infinitesimal to Finite Time Intervals; Re-derivation of the Feynman Path Integrals via the Trotter Formula; Free-Particle Propagator; Continuous Paths but Nowhere Differentiable; Path Integrals for Quadratic Potentials; WKB in the Operatorial Language; WKB in the Path-Integral Language; Introduction to the Formalism of Wigner Functions; Marinov's Path Integral for Wigner Functions; Semiclassical Expansion of Marinov's Work; The Work of Koopman and von Neumann (KvN) on the Operatorial Version of Classical Mechanics; Path Integral for Classical Mechanics (CPI) from the KvN Formalism; Cartan Calculus via the CPI; Geometric Quantization via the CPI; Non-Superposition Principle in Classical Mechanics and Degrees of Freedom; Going Beyond Classical Mechanics;

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Book SynopsisThis book aims to provide a quick pedagogical introduction to path integrals. It contains original material that never before has appeared in a book, for example the path integrals for the Wigner functions and for Classical Mechanics. This application to Classical Mechanics connects different fields like Hamiltonian mechanics and differential geometry, so the book is suitable for students and researchers from various disciplines.Table of ContentsQuantum Mechanics and Summing Up Amplitudes; Double Slit Experiment; Infinite Slits Experiments and Path-Correspondence; Dirac's 1932 Paper on Small Time Amplitudes; Time-Slicing: From Infinitesimal to Finite Time Intervals; Re-derivation of the Feynman Path Integrals via the Trotter Formula; Free-Particle Propagator; Continuous Paths but Nowhere Differentiable; Path Integrals for Quadratic Potentials; WKB in the Operatorial Language; WKB in the Path-Integral Language; Introduction to the Formalism of Wigner Functions; Marinov's Path Integral for Wigner Functions; Semiclassical Expansion of Marinov's Work; Path Integrals for Classical Mechanics Objects (Cyclists); Corresponding Operatorial Version of Classical Mechanics; The Work of Koopman and von Neuman;

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Book SynopsisOrganisms endowed with life show a sense of awareness, interacting with and learning from the universe in and around them. Each level of interaction involves transfer of information of various kinds, and at different levels. Each thread of information is interlinked with the other, and woven together, these constitute the universe — both the internal self and the external world — as we perceive it. They are, figuratively speaking, Nature's longest threads. This volume reports inter-disciplinary research and views on information and its transfer at different levels of organization by reputed scientists working on the frontier areas of science. It is a frontier where physics, mathematics and biology merge seamlessly, binding together specialized streams such as quantum mechanics, dynamical systems theory, and mathematics. The topics would interest a broad cross-section of researchers in life sciences, physics, cognition, neuroscience, mathematics and computer science, as well as interested amateurs, familiarizing them with frontier research on understanding information transfer in living systems.Table of ContentsMathematics In-forms Physics and Physics Per-forms Mathematics: Comments (N Kumar); An Incomplete Summing Up of Quantum Measurements (N D Hari Dass); Predictive Information for Quantum Bio-Systems (Arun Kumar Pati); Quantum Effects in Biological Systems (Sisir Roy); Instabilities in Sensory Processes (J Balakrishnan); Active Cellular Mechanics and Information Processing in the Living Cell (Madan Rao); On the Importance of Length Scales in Determining the Physics of Biological Systems (B Ashok); q-Deformations and the Dynamics of the Larch Bud-Moth Population Cycles (Sudharsana V Iyengar and J Balakrishnan); Newtonian Chimpanzees? A Molecular Dynamics Approach to Understanding Decision Making by Wild Chimpanzees (Matthew Westley, Surajit Sen and Anindya Sinha); Quantum Probability - A New Direction for Modeling in Cognitive Science (Sisir Roy); Knowledge, its Hierarchy and its Direction (Apoorva Patel); Some Remarks on Numbers and their Cognition (P P Divakaran); Conceptual Revolution of the 20th Century Leading to One Grand Unified Concept - The Quantum Vacuum (B V Sreekantan); Classical Coherence, Life and Consciousness (Partha Ghose); Consciousness - A Verifiable Prediction (N Panchapakesan); Goedel, Tarski, Turing and the Conundrum of Free Will (Chetan S Mandayam Nayakar & R Srikanth); Mathematics and Cognition (Rajesh Kasturirangan);

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Book SynopsisIn this book we have solved the complicated problem of constructing upper bounds for many-time averages for the case of a fairly broad class of model systems with four-fermion interaction. The methods proposed in this book for solving this problem will undoubtedly find application not only for the model systems associated with the theory of superconductivity considered here. The theoretical methods developed in Chapters 1 and 2 are already applicable to a much broader class of model systems from statistical physics and the theory of elementary particles.Table of ContentsOn the Theory of Superfluidity; Quasi-Averages in Problems of Statistical Mechanics; Hydrodynamics Equations in Statistical Mechanics; On the Hydrodynamics of a Superfluid Liquid; On the Model Hamiltonian of Superconductivity; Model Hamiltonians with Fermion Interaction;

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Book SynopsisThe Advanced School on Quantum Foundations and Open Quantum Systems was an exceptional combination of lectures. These comprise lectures in standard physics and investigations on the foundations of quantum physics.On the one hand it included lectures on quantum information, quantum open systems, quantum transport and quantum solid state. On the other hand it included lectures on quantum measurement, models for elementary particles, sub-quantum structures and aspects on the philosophy and principles of quantum physics.The special program of this school offered a broad outlook on the current and near future fundamental research in theoretical physics.The lectures are at the level of PhD students.Table of ContentsKerr-Newman Electron as Spinning Soliton (Alexander Burinskii); Elements For the Development of A Darwinian-Like Scheme Leading to Quantum Mechanics (Carlos Baladron); A Geometrical Approach to Dislocation Densities in Semiconductors (K Bakke and F Moraes); The Zero-Point Field and the Emergence of the Quantum (L De La Pena, A M Cetto and A Valdes Hernandez); Emergence of Quantum Mechanics From Sub-Quantum Statistical Mechanics (Gerhard Grossing); Towards Wave Resolution of Wave-Particle Duality (Andrei Khrennikov); Quantum Transport: An Unified Approach Via A Multivariate Hypergeometric Generating Function (A F Macedo-Junior and A M S Macedo); Time-Dependent Coupled Harmonic Oscillators: Classical and Quantum Solutions (D X Macedo and I Guedes); Event-Based Simulation of Quantum Physics Experiments (Kristel Michielsen and Hans De Raedt); Lectures on Dynamical Models For Quantum Measurements (T M Nieuwenhuizen, M Perarnau Llobet and R Balian); Physics of Quantum Computing (Elisabetta Paladino and Giuseppe Falci); Reality, Causality, and Probability, From Quantum Mechanics to Quantum Field Theory: Lectures on the Epistemology of Quantum Theory (Arkady Plotnitsky); Quantum Information in Communication and Imaging (David Simon, Gregg Jaeger and Alexander V Sergienko); Green's Function Technics in the Solid State (Vaclav Spicka);

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Book SynopsisThe book originated in a series of lectures given at Liverpool in 2013 to a group that included postgraduate and undergraduate students and staff of the Physics Department. They followed from two very successful lectures given to the undergraduate Physical Society. It seemed that there was a very large interest among the students in investigating the foundations of physics in a way that was never done in physics courses, and was not available in books or other outlets. However, the idea was to create a framework in which students (and interested staff) could develop their own thinking relative to the ideas in the lectures. So it was important to create both conceptual and mathematical structures on the issues that are important at this level. The book has the right sort of technical content to allow for this development, but doesn't lose itself in excessive details. The ideal use for this book would be on postgraduate courses where students would be encouraged to think about the foundations in a way that is well beyond the superficial. However, a course on aspects of this material would also be valuable at the undergraduate level, where students could be stimulated into believing that creative thinking could solve the problems that emerge when we confront foundational problems.Table of ContentsIntroduction to Foundational Physics; Mathematical Ideas and Methods; The Most Primitive Concepts; A Fundamental Symmetry; Nilpotent Quantum Mechanics I-II; Nilpotent Quantum Field Theory; Gravity; Particles; Return to Symmetries;

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Book SynopsisOur understanding of the physical world was revolutionized in the twentieth century — the era of “modern physics”. Two books by the second author entitled Introduction to Modern Physics: Theoretical Foundations and Advanced Modern Physics: Theoretical Foundations, aimed at the very best students, present the foundations and frontiers of today's physics. Many problems are included in these texts. A previous book by the current authors provides solutions to the over 175 problems in the first volume.A third volume Topics in Modern Physics: Theoretical Foundations has recently appeared, which covers several subjects omitted in the essentially linear progression in the previous two. This book has three parts: part 1 is on quantum mechanics, part 2 is on applications of quantum mechanics, and part 3 covers some selected topics in relativistic quantum field theory. Parts 1 and 2 follow naturally from the initial volume. The present book provides solutions to the over 135 problems in this third volume.The three volumes in this series, together with the solutions manuals, provide a clear, logical, self-contained, and comprehensive base from which students can learn modern physics. When finished, readers should have an elementary working knowledge in the principal areas of theoretical physics of the twentieth century.Table of ContentsIntroduction; Quantum Mechanics: Solutions to the Schrodinger Equation; Formal Developments; Applications of Quantum Mechanics: Approximation Methods for Bound States; Scattering Theory; Time-Dependent Perturbation Theory; Electromagnetic Radiation and Quantum Electrodynamics; Relativistic Quantum Field Theory: Discrete Symmetries; Heisenberg Picture; Feynman Rules for QCD; Problems and Appendices: The Two-Body Problem; Charged Particle in External Electromagnetic Field;

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Book Synopsis'Kenneth Wilson was a brilliant and creative contributor to the work on renormalization groups and phase transitions. He applied his multifaceted genius to condensed matter physics as well as nuclear and elementary particle physics.'by Murray Gell-MannThe purpose of bringing out this volume is to commemorate the memory of Ken Wilson and to preserve the legacy of his ground-breaking advances. This volume brings together a collection of articles written by colleagues of Ken Wilson as well as fellow physicists and scholars — some of who knew him personally and others who are knowledgeable about his sterling contributions to the foundations of theoretical physics.To commemorate the memory of Ken Wilson, many leading and illustrious physicists have contributed to this volume — Ian Affleck, Belal E Baaquie, Ken Bowler, Édouard Brézin, Tohru Eguchi, Michael E Fisher, Paul Ginsparg, Domenico Giuliano, Stanislaw Glazek, Bailin Hao, Kerson Huang, Roman Jackiw, Richard Kenway, H R Krishnamurthy, N D Mermin, Stuart Pawley, Michael Peskin, Alexander Polyakov, John Schwarz, R Shankar, Akira Ukawa, David Wallace, Franz Wegner, Steven Weinberg, and Anthony Zee.Table of ContentsLattice Gauge Theory and the Large N Reduction (Tohru Eguchi); A Critical History of Renormalization (Kerson Huang); Ken Wilson - The Early Years (Roman Jackiw); Skeleton Graph Expansion of Critical Exponents in "Cultural Revolution" Years (Hao Bailin); Renormalization Group Theory: Its Basis and Formulation in Statistical Physics (Michael E Fisher); Effective Field Theory, Past and Future (Steven Weinberg); In Memory of Kenneth G Wilson (Franz J Wegner); and other papers;

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Book Synopsis'Kenneth Wilson was a brilliant and creative contributor to the work on renormalization groups and phase transitions. He applied his multifaceted genius to condensed matter physics as well as nuclear and elementary particle physics.'by Murray Gell-MannThe purpose of bringing out this volume is to commemorate the memory of Ken Wilson and to preserve the legacy of his ground-breaking advances. This volume brings together a collection of articles written by colleagues of Ken Wilson as well as fellow physicists and scholars — some of who knew him personally and others who are knowledgeable about his sterling contributions to the foundations of theoretical physics.To commemorate the memory of Ken Wilson, many leading and illustrious physicists have contributed to this volume — Ian Affleck, Belal E Baaquie, Ken Bowler, Édouard Brézin, Tohru Eguchi, Michael E Fisher, Paul Ginsparg, Domenico Giuliano, Stanislaw Glazek, Bailin Hao, Kerson Huang, Roman Jackiw, Richard Kenway, H R Krishnamurthy, N D Mermin, Stuart Pawley, Michael Peskin, Alexander Polyakov, John Schwarz, R Shankar, Akira Ukawa, David Wallace, Franz Wegner, Steven Weinberg, and Anthony Zee.Table of ContentsLattice Gauge Theory and the Large N Reduction (Tohru Eguchi); A Critical History of Renormalization (Kerson Huang); Ken Wilson - The Early Years (Roman Jackiw); Skeleton Graph Expansion of Critical Exponents in "Cultural Revolution" Years (Hao Bailin); Renormalization Group Theory: Its Basis and Formulation in Statistical Physics (Michael E Fisher); Effective Field Theory, Past and Future (Steven Weinberg); In Memory of Kenneth G Wilson (Franz J Wegner); and other papers;

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Book SynopsisLight and Vacuum presents a synthesis of selected fundamental topics of electromagnetic wave theory and quantum electrodynamics (QED) and analyzes the main theoretical difficulties encountered to ensure a coherent mathematical description of the simultaneous wave-particle nature of light, put in evidence by the experiments. The notion and the role of the quantum vacuum, strongly related to light, are extensively investigated.Classical electrodynamics issued from Maxwell's equations revealed the necessity of introducing the notion of volume for an electromagnetic wave to stand entailing precise values of cut-off wavelengths to account for the shape and dimensions of the surrounding space. Conversely, in QED, light is considered to be composed of point particles disregarding the conceptual question on how the frequency of oscillating electric and magnetic fields may be attributed to a point particle.To conciliate these concepts, the book provides a comprehensive overview of the author's work, including innovative contributions on the quantization of the vector potential amplitude at a single photon state, the non-local simultaneous wave-particle mathematical representation of the photon and finally the quantum vacuum. The purpose of the advanced elaborations is to raise questions, give hints and answers, and finally aspire for further theoretical and experimental studies in order to improve our knowledge and understanding on the real essence of Light and Vacuum.Table of ContentsIntroduction; Historical Survey and Experimental Evidence; Basic Principles of the Electromagnetic Wave Theory; From Electromagnetic Waves to Quantum Electrodynamics; Theory, Experiments and Questions; Analysis of the Electromagnetic Field Quantization Process and the Photon Vector Potential. The Non-Local Photon Wave-Particle Representation and the Quantum Vacuum; Epilogue;

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