Description
Book SynopsisApplications of quantum field theoretical methods to gravitational physics, both in the semiclassical and the full quantum frameworks, require a careful formulation of the fundamental basis of quantum theory, with special attention to such important issues as renormalization, quantum theory of gauge theories, and especially effective action formalism. The first part of this graduate textbook provides both a conceptual and technical introduction to the theory of quantum fields. The presentation is consistent, starting from elements of group theory, classical fields, and moving on to the effective action formalism in general gauge theories. Compared to other existing books, the general formalism of renormalization in described in more detail, and special attention paid to gauge theories. This part can serve as a textbook for a one-semester introductory course in quantum field theory. In the second part, we discuss basic aspects of quantum field theory in curved space, and perturbative quantum gravity. More than half of Part II is written with a full exposition of details, and includes elaborated examples of simplest calculations. All chapters include exercises ranging from very simple ones to those requiring small original investigations. The selection of material of the second part is done using the must-know principle. This means we included detailed expositions of relatively simple techniques and calculations, expecting that the interested reader will be able to learn more advanced issues independently after working through the basic material, and completing the exercises.
Trade ReviewIt is a good moment for summarizing the various advances, and these two authors are among the best experts in the specific field of quantum effective actions in gravity. * Michele Maggiore, University of Geneva *
The subject of the book is timely, especially since many results of quantum field theory are actively used in modern cosmology, and both authors have long-time experience of teaching courses on the subject at several universities. * Valeri Frolov, University of Alberta *
Table of ContentsPART I INTRODUCTION TO QUANTUM FIELD THEORY 1: Introduction 2: Relativistic Symmetry 3: Lagrange formalism in field theory 4: Field Models 5: Canonical Quantization of Free Fields 6: Scattering Matrix and Green Functions 7: Functional Integrals 8: Perturbation Theory 9: Renormalization 10: Quantum Gauge Theories PART II SEMICLASSICAL AND QUANTUM GRAVITY MODELS 11: Brief Review of General Relativity. 12: Classical fields in curved spacetime 13: Quantum fields in curved spacetime: renormalization 14: One-loop divergences 15: Renormalization group in curved space 16: Non-local form factors in flat and curved spacetime 17: Conformal anomaly and anomaly-induced action 18: General Notions of Perturbative Quantum Gravity 19: Massive ghosts in higher derivative models 20: One-loop renormalization in quantum gravity 21: Renormalization group in perturbative quantum gravity 22: Induced gravity approach 23: Final remarks on Part II References PART I INTRODUCTION TO QUANTUM FIELD THEORY 1: Introduction 2: Relativistic Symmetry 3: Lagrange formalism in field theory 4: Field Models 5: Canonical Quantization of Free Fields 6: Scattering Matrix and Green Functions 7: Functional Integrals 8: Perturbation Theory 9: Renormalization 10: Quantum Gauge Theories PART II SEMICLASSICAL AND QUANTUM GRAVITY MODELS 11: Brief Review of General Relativity. 12: Classical fields in curved spacetime 13: Quantum fields in curved spacetime: renormalization 14: One-loop divergences 15: Renormalization group in curved space 16: Non-local form factors in flat and curved spacetime 17: Conformal anomaly and anomaly-induced action 18: General Notions of Perturbative Quantum Gravity 19: Massive ghosts in higher derivative models 20: One-loop renormalization in quantum gravity 21: Renormalization group in perturbative quantum gravity 22: Induced gravity approach 23: Final remarks on Part II References
