Theory of interacting quantum fields / Alexei L. Rebenko.

Format:

Book

Author/Creator:

Rebenko, Alekseĭ Lukich.

Contributor:

Malyshev, Peter V.

Series:

De Gruyter Studies in Mathematics

De Gruyter studies in mathematics, 0179-0986 ; 39

De Gruyter Studies in Mathematics ; 39

Language:

English

Subjects (All):

Quantum field theory.

Physical Description:

1 online resource (588 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; Boston : De Gruyter, c2012.

Language Note:

English

Summary:

This monograph is devoted to the systematic presentation of foundations of the quantum field theory. Unlike numerous monographs devoted to this topic, a wide range of problems covered in this book are accompanied by their sufficiently clear interpretations and applications. An important significant feature of this monograph is the desire of the author to present mathematical problems of the quantum field theory with regard to new methods of the constructive and Euclidean field theory that appeared in the last thirty years of the 20th century and are based on the rigorous mathematical apparatus of functional analysis, the theory of operators, and the theory of generalized functions. The monograph is useful for students, post-graduate students, and young scientists who desire to understand not only the formality of construction of the quantum field theory but also its essence and connection with the classical mechanics, relativistic classical field theory, quantum mechanics, group theory, and the theory of path integral formalism.

Contents:

Frontmatter

Preface

Notation

Contents

Chapter 0. Introduction

Part I. Symmetry Groups of Elementary Particles

Chapter 1. Lorentz Group

Chapter 2. Groups of Internal Symmetries

Chapter 3. Problems to Part I

Part II. Classical Theory of the Free Fields

Chapter 4. Lagrangian and Hamiltonian Formalisms of the Classical Field Theory

Chapter 5. Classical Theory of Free Scalar Fields

Chapter 6. Spinor Field

Chapter 7. Vector Fields

Chapter 8. Electromagnetic Field

Chapter 9. Equations for Fields with Higher Spins

Chapter 10. Problems to Part II

Part III. Classical Theory of Interacting Fields

Chapter 11. Gauge Theory of the Electromagnetic Interaction

Chapter 12. Classical Theory of Yang-Mills Fields

Chapter 13. Masses of Particles and Spontaneous Breaking of Symmetry

Chapter 14. On the Construction of the General Lagrangian of Interacting Fields

Chapter 15. Solutions of the Equations for Classical Fields: Solitary Waves, Solitons, Instantons

Chapter 16. Problems to Part III

Part IV. Second Quantization of Fields

Chapter 17. Axioms and General Principles of Quantization

Chapter 18. Quantization of the Free Scalar Field

Chapter 19. Quantization of the Free Spinor Field

Chapter 20. Quantization of the Vector and Electromagnetic Fields. Specific Features of the Quantization of Gauge Fields

Chapter 21. CPT. Spin and Statistics

Chapter 22. Representations of Commutation and Anticommutation Relations

Chapter 23. Green Functions

Chapter 24. Problems to Part IV

Part V. Quantum Theory of Interacting Fields. General Problems

Chapter 25. Construction of Quantum Interacting Fields and Problems of This Construction

Chapter 26. Scattering Theory. Scattering Matrix

Chapter 27. Equations for Coefficient Functions of the S-Matrix

Chapter 28. Green Functions and Scattering Matrix

Chapter 29. On Renormalization in Perturbation Theory

Chapter 30. Method of Functional (Path) Integrals in Quantized Field Theory

Chapter 31. Problems to Part V

Part VI. Axiomatic and Euclidean Field Theories

Chapter 32. Wightman Axiomatics

Chapter 33. Other Axiomatic Approaches

Chapter 35. Euclidean Axiomatics

Chapter 36. Problems to Part VI

Part VII. Quantum Theory of Gauge Fields

Chapter 37. Quantum Electrodynamics (QED)

Chapter 38. Quantization of Gauge Fields

Chapter 39. Standard Models of Interactions

Chapter 40. Problems to Part VII

Appendix. Hints for the Solution of Problems

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [549]-561) and index.

ISBN:

9786613940094

9781283627641

1283627647

9783119163378

3119163376

OCLC:

993343088