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Introduction to Quantum Field Theory with Applications to Quantum Gravity

ΣΥΓΓΡΑΦΕΙΣ

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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.

**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**

Περιγραφή

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.

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