Theory of Interacting Quantum Fields

Alexei L. Rebenko

Published by De Gruyter 2012

Theory of Interacting Quantum Fields

Alexei L. Rebenko
Translated by: Peter V. Malyshev

Volume 39 in the series De Gruyter Studies in Mathematics

https://doi.org/10.1515/9783110250633

Overview
Contents

About this book

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.

Author / Editor information

Alexei L. Rebenko, Department of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine.

Reviews

"Overall, it seems to me that it [the book] strives to strike a balance between mathematics and physics. It is well written, and the presentation and the discussion of the individual arguments are good. In my opinion, this is indeed an excellent reference book. If you want to pick some specific argument, look at the index; you will find it and (most importantly) you will understand it. [...] The explanations are excellent: the teaching experience of the author is indubitable. [...] All in all, it is a good book." Mathematical Reviews

"This self-contained, comprehensive monograph presents a careful modern introduction to the basic methods and applications of quantum field theory. [...] This book should be useful as a reference for students and researchers alike with interests in QFT, particle physics, mathematics and related areas." Zentralblatt für Mathematik

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Preface Requires Authentication Unlicensed Licensed Download PDF	v
Notation Requires Authentication Unlicensed Licensed Download PDF	viii
Contents Requires Authentication Unlicensed Licensed Download PDF	xi
Chapter 0. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
Part I. Symmetry Groups of Elementary Particles
Chapter 1. Lorentz Group Requires Authentication Unlicensed Licensed Download PDF	7
Chapter 2. Groups of Internal Symmetries Requires Authentication Unlicensed Licensed Download PDF	23
Chapter 3. Problems to Part I Requires Authentication Unlicensed Licensed Download PDF	35
Part II. Classical Theory of the Free Fields
Chapter 4. Lagrangian and Hamiltonian Formalisms of the Classical Field Theory Requires Authentication Unlicensed Licensed Download PDF	39
Chapter 5. Classical Theory of Free Scalar Fields Requires Authentication Unlicensed Licensed Download PDF	61
Chapter 6. Spinor Field Requires Authentication Unlicensed Licensed Download PDF	82
Chapter 7. Vector Fields Requires Authentication Unlicensed Licensed Download PDF	128
Chapter 8. Electromagnetic Field Requires Authentication Unlicensed Licensed Download PDF	135
Chapter 9. Equations for Fields with Higher Spins Requires Authentication Unlicensed Licensed Download PDF	149
Chapter 10. Problems to Part II Requires Authentication Unlicensed Licensed Download PDF	152
Part III. Classical Theory of Interacting Fields
Chapter 11. Gauge Theory of the Electromagnetic Interaction Requires Authentication Unlicensed Licensed Download PDF	157
Chapter 12. Classical Theory of Yang–Mills Fields Requires Authentication Unlicensed Licensed Download PDF	164
Chapter 13. Masses of Particles and Spontaneous Breaking of Symmetry Requires Authentication Unlicensed Licensed Download PDF	171
Chapter 14. On the Construction of the General Lagrangian of Interacting Fields Requires Authentication Unlicensed Licensed Download PDF	181
Chapter 15. Solutions of the Equations for Classical Fields: Solitary Waves, Solitons, Instantons Requires Authentication Unlicensed Licensed Download PDF	191
Chapter 16. Problems to Part III Requires Authentication Unlicensed Licensed Download PDF	197
Part IV. Second Quantization of Fields
Chapter 17. Axioms and General Principles of Quantization Requires Authentication Unlicensed Licensed Download PDF	201
Chapter 18. Quantization of the Free Scalar Field Requires Authentication Unlicensed Licensed Download PDF	218
Chapter 19. Quantization of the Free Spinor Field Requires Authentication Unlicensed Licensed Download PDF	222
Chapter 20. Quantization of the Vector and Electromagnetic Fields. Specific Features of the Quantization of Gauge Fields Requires Authentication Unlicensed Licensed Download PDF	225
Chapter 21. CPT. Spin and Statistics Requires Authentication Unlicensed Licensed Download PDF	240
Chapter 22. Representations of Commutation and Anticommutation Relations Requires Authentication Unlicensed Licensed Download PDF	250
Chapter 23. Green Functions Requires Authentication Unlicensed Licensed Download PDF	274
Chapter 24. Problems to Part IV Requires Authentication Unlicensed Licensed Download PDF	287
Part V. Quantum Theory of Interacting Fields. General Problems
Chapter 25. Construction of Quantum Interacting Fields and Problems of This Construction Requires Authentication Unlicensed Licensed Download PDF	291
Chapter 26. Scattering Theory. Scattering Matrix Requires Authentication Unlicensed Licensed Download PDF	298
Chapter 27. Equations for Coefficient Functions of the S-Matrix Requires Authentication Unlicensed Licensed Download PDF	327
Chapter 28. Green Functions and Scattering Matrix Requires Authentication Unlicensed Licensed Download PDF	336
Chapter 29. On Renormalization in Perturbation Theory Requires Authentication Unlicensed Licensed Download PDF	358
Chapter 30. Method of Functional (Path) Integrals in Quantized Field Theory Requires Authentication Unlicensed Licensed Download PDF	391
Chapter 31. Problems to Part V Requires Authentication Unlicensed Licensed Download PDF	416
Part VI. Axiomatic and Euclidean Field Theories
Chapter 32. Wightman Axiomatics Requires Authentication Unlicensed Licensed Download PDF	421
Chapter 33. Other Axiomatic Approaches Requires Authentication Unlicensed Licensed Download PDF	429
Chapter 35. Euclidean Axiomatics Requires Authentication Unlicensed Licensed Download PDF	453
Chapter 36. Problems to Part VI Requires Authentication Unlicensed Licensed Download PDF	460
Part VII. Quantum Theory of Gauge Fields
Chapter 37. Quantum Electrodynamics (QED) Requires Authentication Unlicensed Licensed Download PDF	465
Chapter 38. Quantization of Gauge Fields Requires Authentication Unlicensed Licensed Download PDF	498
Chapter 39. Standard Models of Interactions Requires Authentication Unlicensed Licensed Download PDF	521
Chapter 40. Problems to Part VII Requires Authentication Unlicensed Licensed Download PDF	542
Appendix. Hints for the Solution of Problems Requires Authentication Unlicensed Licensed Download PDF	544
Bibliography Requires Authentication Unlicensed Licensed Download PDF	549
Index Requires Authentication Unlicensed Licensed Download PDF	562

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Mathematical Physicists, Theoretical Physicists, Mathematicians; PhD Students in Mathematics and Physics; Academic Libraries
Pages
- Front matter: 20
- Main content: 568
Illustrations
- Illustrations: 30
- Tables: 1
Keywords: Bernstein Function; Semigroup; Operator Theory; Probability Measure; Monotonic Function

eBook

Published: July 4, 2012
ISBN: 9783110250633

Hardcover

Published: June 14, 2012
ISBN: 9783110250626