Lectures on Quantum Field Theory. Ashok Das
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LECTURES ON QUANTUM FIELD THEORY
Second Edition
Copyright © 2021 by World Scientific Publishing Co. Pte. Ltd.
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ISBN 978-981-122-086-9 (hardcover)
ISBN 978-981-122-216-0 (paperback)
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ISBN 978-981-122-088-3 (ebook for individuals)
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Printed in Singapore
To
My friends and collaborators
Josif and Susumu
and
to
Ever caring and charming
Kiron and Momo
Preface
Preface to the First Edition
Over the past several years I have taught a two-semester graduate course on quantum field theory at the University of Rochester. In this course the ideas of quantum field theory are developed in a traditional manner through canonical quantization. This book consists of my lectures in this course. At Rochester, we also teach a separate course on quantum field theory based on the path integral approach and my lectures in that course have already been published by World Scientific in
A. Das, Field Theory: A Path Integral Approach (Second Edition), World Scientific, Singapore (2006).
The material in the present book should be thought of as complementary to this earlier book. In fact, in the present lectures, there is no attempt to develop the path integral methods, rather we use the results from path integrals with a brief discussion when needed.
The topics covered in the present book contain exactly the material discussed in the two-semester course except for Chapter 10 (Dirac quantization) and Chapter 11 (Discrete symmetries) which have been added for completeness and are normally discussed in another course. Quantum field theory is a vast subject and only selected topics, which I personally feel every graduate student in the subject should know, have been covered in these lectures. Needless to say, there are many other important topics which have not been discussed because of time constraints in the course (and space constraints in the book). However, all the material covered in this book has been presented in an informal (classroom like) setting with detailed derivations which should be helpful to students.
A book of this size is bound to have many possible sources of error. However, since my lectures have already been used by various people in different universities, I have been fortunate to have their feedback which I have incorporated into the book. In addition, several other people have read all the chapters carefully and I thank them all for their comments. In particular, it is a pleasure for me to thank Ms. Judy Mack and Professor Susumu Okubo for their tireless effort in going through the entire material. I am personally grateful to Dr. John Boersma for painstakingly and meticulously checking all the mathematical derivations. Of course, any remaining errors and typos are my own.
Like the subject itself, the list of references to topics in quantum field theory is enormous and it is simply impossible to do justice to everyone who has contributed to the growth of the subject. I have in no way attempted to give an exhaustive list of references to the subject. Instead I have listed only a few suggestive references at the end of each chapter in the hope that the readers can get to the other references from these sources.
The Feynman graphs in this book were drawn using Jaxodraw while most other figures were generated using PSTricks. I am grateful to the people who developed these extremely useful softwares. Finally, I would like to thank Dave Munson for helping out with various computer related problems.
Ashok Das,
Rochester
Preface to the Second Edition
This second edition of the book grew out of requests, by students and colleagues alike from all over the world, to include a wide range of related interesting topics. However, it was not at all practical to accommodate all the topics that were requested since the first edition of the book already had about 775 pages. I have only been able to fulfill only a few of the requests which, I believed, would fit in nicely with the logic of the earlier edition. There are two new chapters as well as two appendices in this new edition and that has enlarged the book by about 150 pages. One of the two chapters added discusses Nielsen identities which addresses questions of gauge independence of physical parameters such as mass of a particle as well as other physical parameters derived from the effective potential which itself is gauge dependent. The other chapter discusses global supersymmetry which is a very important idea and which was requested by many readers. One of the two appendices discusses fermions in arbitrary dimensions (as well as in four dimensions). In particular, it investigates the number of space-time dimensions where Majorana, Weyl and Majorana-Weyl fermions can exist. The second appendix discusses the question of gauge invariant (gauge) potentials in detail as well as the Fock-Schwinger gauge as an implementable, complete and ghost free gauge which is widely used in nonperturbative calculations of condensates. In addition, the material of the earlier edition of the book has also been revised and expanded wherever necessary to make explanations simpler and easier.
I would like to thank Dr. Pushpa Kalauni for going through the material carefully and Dave Munson for all the technical help with LaTex.
Ashok Das,
Rochester
Contents