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Classical Covariant Fields / Edition 1

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This book discusses the classical foundations of field theory, using the language of variational methods and covariance. There is no other book which gives such a comprehensive overview of the subject, exploring the limits of what can be achieved with purely classical notions. These classical notions have a deep and important connection with the second quantized field theory, which is shown to follow 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. It uses a well documented set of conventions and catalogues results which are often hard to find in the literature. Care is taken to explain how results arise and how to interpret results physically, for graduate students starting out in the field. Many physical examples are provided, making the book an ideal supplementary text for courses on elementary field theory, group theory and dynamical systems. It will also be a valuable reference for researchers already working in these and related areas.
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Editorial Reviews

From The Critics
Burgess (theoretical physics, Oslo U. College) compiles notes and unpublished results he has accumulated on classical field theory into a reference for himself and other researchers and graduate students. He presents general theory accompanied by specific examples, separates logically independent ideas, and uses a consistent notation. Among hit topics are the action principle, statistical interpretation of the field, spacetime transformations, unified kinematics and dynamics, and the real Klein-Gordon field (but also the complex version). He appends useful formulae and a list of recommended reading. Annotation c. Book News, Inc., Portland, OR (
From the Publisher
"There are two features which make this book a really unique source on this subject. It is very detailed. It seems that nothing has escaped the author's attention. Also, this book is very explicit. All notation and conventions are carefully introduced. In many cases, more abstract formulae are accompanied by their component forms. These two features make this book very convenient to use in research and teaching. I greatly recommend this book as a supplementary text for courses on field theory, group theory, dynamical systems, and particle physics." Mathematical Reviews
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Product Details

  • ISBN-13: 9780521675772
  • Publisher: Cambridge University Press
  • Publication date: 7/31/2005
  • Series: Cambridge Monographs on Mathematical Physics Series
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 552
  • Product dimensions: 6.85 (w) x 9.72 (h) x 1.10 (d)

Meet the Author

Mark Burgess obtained his PhD in theoretical physics from the University of Newcastle Upon Tyne in 1990. He held a Royal Society fellowship at the University of Oslo from 1991 to 1992 and then had a two-year postdoctoral fellowship from the Norwegian Research Council. Since 1994 he has been an associate professor at Oslo University College. Dr Burgess has been invited to lecture at universities and institutes throughout the world, and has published numerous articles, as well as five previous books.

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Table of Contents

Pt. 1 Fields 1
1 Introduction 3
2 The electromagnetic field 9
3 Field parameters 32
4 The action principle 50
5 Classical field dynamics 72
6 Statistical interpretation of the field 113
7 Examples and applications 131
Pt. 2 Groups and fields 167
8 Field transformations 169
9 Spacetime transformations 207
10 Kinematical and dynamical transformations 256
11 Position and momentum 283
12 Charge and current 325
13 The non-relativistic limit 340
14 Unified kinematics and dynamics 358
15 Epilogue: quantum field theory 390
Pt. 3 Reference: a compendium of fields 397
16 Gallery of definitions 399
17 The Schrodinger field 410
18 The real Klein-Gordon field 416
19 The complex Klein-Gordon field 425
20 The Dirac field 430
21 The Maxwell radiation field 452
22 The massive Proca field 464
23 Non-Abelian fields 466
24 Chern-Simons theories 486
25 Gravity as a field theory 491
Pt. 4 Appendices 499
App. A Useful formulae 501
App. B: Recommended reading 513
References 515
Index 521
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