Processes in the lowest order of the perturbation theory
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Voja Radovanovi´c
Problem Book in Quantum Field Theory Second Edition
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Voja Radovanovi´c Faculty of Physics University of Belgrade Studentski trg 12-16 11000 Belgrade Serbia and Montenegro E-mail: [email protected]
Library of Congress Control Number: 2007940156 ISBN 978-3-540-77013-8 Springer Berlin Heidelberg New York ISBN 978-3-540-29062-9 1st ed. Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2008 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the author using a Springer LATEX macro package Cover design: eStudio Calamar, Spain Printed on acid-free paper
SPIN: 12197873
543210
To my daughter Natalija
Preface
This Problem Book is based on the exercises and lectures which I have given to undergraduate and graduate students of the Faculty of Physics, University of Belgrade over many years. Nowadays, there are a lot of excellent Quantum Field Theory textbooks. Unfortunately, there is a shortage of Problem Books in this field, one of the exceptions being the Problem Book of Cheng and Li [7]. The overlap between this Problem Book and [7] is very small, since the latter mostly deals with gauge field theory and particle physics. Textbooks usually contain problems without solutions. As in other areas of physics doing more problems in full details improves both understanding and efficiency. So, I feel that the absence of such a book in Quantum Field Theory is a gap in the literature. This was my main motivation for writing this Problem Book. To students: You cannot start to do problems without previous studying your lecture notes and textbooks. Try to solve problems without using solutions; they should help you to check your results. The level of this Problem Book corresponds to the textbooks of Mandl and Show [15]; Greiner and Reinhardt [11] and Peskin and Schroeder [16]. Each Chapter begins with a short introduction aimed to define notation. The first Chapter is devoted to the Lorentz and Poincar´e symmetries. Chapters 2, 3 and 4 deal with the relativistic quantum mechanics with a special emphasis on the Dirac equation. In Chapter 5 we present problems related to the Euler-Lagrange equations and the Noether theor
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