Classical Covariant Fields

This 2002 OA monograph discusses the classical foundations of field theory, using the language of variational methods and covariance.

Mark Burgess (Author)

9781009289900, Cambridge University Press

Hardback, published 9 February 2023

75 pages
25 x 17.6 x 3.5 cm, 1.11 kg

'In conclusion, I think that this book can be valuable for graduate students in physics, mainly interested in quantum field theories and particle physics, who will appreciate an exhaustive description of the classical foundations of such theories.' Zentralblatt MATH

This 2002 book discusses the classical foundations of field theory, using the language of variational methods and covariance. It explores the limits of what can be achieved with purely classical notions, and shows how these have a deep and important connection with the second quantized field theory, which follows on from the Schwinger Action Principle. The book takes a pragmatic view of field theory, focusing on issues which are usually omitted from quantum field theory texts and cataloging results which are hard to find in the literature. Care is taken to explain how results arise and how to interpret them physically, for graduate students starting out in the field. An ideal supplementary text for courses on elementary field theory, group theory and dynamical systems, it is also a valuable reference for researchers working in these and related areas. It has been reissued as an Open Access publication on Cambridge Core.

Foreword
Part I. Fields: 1. Introduction
2. The electromagnetic field
3. Field parameters
4. The action principle
5. Classical field dynamics
6. Statistical interpretation of the field
7. Examples and applications
Part II. Groups and Fields: 8. Field transformations
9. Spacetime transformations
10. Kinematical and dynamical transformations
11. Position and momentum
12. Charge and current
13. The non-relativistic limit
14. Unified kinematics and dynamics
15. Epilogue: quantum field theory
Part III. Reference: A Compendium of Fields: 16. Gallery of definitions
17. The Schrödinger field
18. The real Klein Gordon field
19. The complex Klein Gordon field
20. The Dirac field
21. The Maxwell radiation field
22. The massive Proca field
23. Non-Abelian fields
24. Chern-Simons theories
25. Gravity as a field theory
Part IV. Appendices.

Subject Areas: Physics [PH]