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Applications 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.
List of contents
- 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
About the author
Iosif L. Buchbinder graduated from Tomsk State University (Russia) with the highest degree (1988, doctor of ciences) in Physical and Mathematical ciences. From 1988 to the present time, he is a professor and head of Department of Theoretical Physics at Tomsk State Pedagogical University. He was a visiting professor at University of Pennsylvania, University of Maryland, University of North Carolina, University of Hannover, Humboldt University Berlin, Cambridge University, University of Sao Paulo, University of Juiz de Fora, University of Hiroshima, Wroclaw University, University of Brno, University of Beer Sheva. Was a supervisor of 21 Ph.D thesis, co-author of Effective Action in Quantum Gravity (IOPP, 1992; with S.D. Odintsov and I.L. Shapiro) and Ideas and Methods of Supersymmetry and Supergravity (IOPP, 1995, 1998; with S.M. Kuzenko), and author of around 300 papers in Statistical Mechanics, Quantum Field Theory, Quantum Gravity, Supersymmetry and Supergravity, and Higher Spin Field Theory.
Ilya Shapiro graduated from Tomsk State University Physics (Russia) with the highest degree (1993, doctor of sciences) in Physical and Mathematical Sciences. In 1994-1996 was post-doc in the Department of Theoretical Physics in the University of Zaragoza, from 1996 visiting and from 2000 permanent professor at the Federal University of Juiz de Fora, Brazil. In 2014 he was visiting professor at the University of Geneva. Between 1985 and 2020 he supervised 13 Ph.D. theses, and has been author and co-author of 150+ articles and three books, including Effective Action In Quantum Gravity (IOPP, 1992), an introductory textbook on Newtonian Mechanics (two editions, in Brazil and in Germany), and an introductory textbook on Tensors and Relativity (Springer, 2019).
Summary
This textbook presents a detailed introduction to the general concepts of quantum field theory, with special emphasis on principal aspects of functional methods and renormalization in gauge theories, and includes an introduction to semiclassical and perturbative quantum gravity in flat and curved spacetimes.
Additional text
The book under review focuses on the theoretical studies of quantum field theory. The book is a well-organized text divided into two parts and 22 chapters, comprising about 530 pages. Its aim, as reflected in its table of contents, which is accessible online, is to provide readers with a solid foundation for approaching quantum field theory in curved spacetime, semiclassical gravity, and perturbative quantum gravity.
Report
It 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
