Introduction to Quantum Field Theory with Applications to Quantum Gravity
Published on 9. February 2023
Book
Paperback/Softback
544 pages
978-0-19-887234-4 (ISBN)
Description
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.
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.
Reviews / Votes
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 * 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 *More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Target group
Professional and scholarly
Illustrations
Various b/w line drawings
Dimensions
Height: 246 mm
Width: 173 mm
Thickness: 29 mm
Weight
1098 gr
ISBN-13
978-0-19-887234-4 (9780198872344)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Ioseph Buchbinder graduated from Tomsk State University (Russia) with the highest degree (1988, doctor of sciences) 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).
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).
Content
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
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
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