Quantum Field Theory I: Basics in Mathematics and Physics A Bridge b
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. The book tries to bridge the existing gap between the dif
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Eberhard Zeidler
Quantum Field Theory I: Basics in Mathematics and Physics A Bridge between Mathematicians and Physicists
Eberhard Zeidler Max Planck Institute for Mathematics in the Sciences Inselstr. 22-26 04103 Leipzig Germany
ISBN 978-3-540-34762-0 e-ISBN 978-3-540-34764-4 DOI 10.1007/978-3-540-34764-4 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2006929535 Mathematics Subject Classification (2000): 35QXX, 58-XX, 81TXX, 82-XX, 83CXX c Springer-Verlag Berlin Heidelberg 2006, Corrected 2nd printing 2009 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 to prosecution under the German Copyright Law. 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. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
¨ TO THE MEMORY OF JURGEN MOSER (1928–1999)
Preface
Daß ich erkenne, was die Welt im Innersten zusammenh¨ alt.1 Faust Concepts without intuition are empty, intuition without concepts is blind. Immanuel Kant (1724–1804) The greatest mathematicians like Archimedes, Newton, and Gauss have always been able to combine theory and applications into one. Felix Klein (1849–1925)
The present comprehensive introduction to the mathematical and physical aspects of quantum field theory consists of the following six volumes: Volume Volume Volume Volume Volume Volume
I: Basics in Mathematics and Physics II: Quantum Electrodynamics III: Gauge Theory IV: Quantum Mathematics V: The Physics of the Standard Model VI: Quantum Gravity and String Theory.
Since ancient times, both physicists and mathematicians have tried to understand the forces acting in nature. Nowadays we know that there exist four fundamental forces in nature: • • • •
Newton’s gravitational force, Maxwell’s electromagnetic force, the strong force between elementary particles, and the weak force between elementary particles (e.g., the force responsible for the radioactive decay of atoms).
In the 20th century, physicists established two basic models, namely, • the Standard Model in cosmology based on Einstein’s theory of general relativity, and • the Standard Model in elementary particle physics based on gauge theory. 1
So that I may perceive whatever holds the world together in its inmost folds. The alchemist Georg Faust (1480–1540) is the protagonist of G
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