Green's Functions And Ordered Exponentials

GREEN’S FUNCTIONS AND ORDERED EXPONENTIALS This book presents a functional approach to the construction, use and approximation of Green’s functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. In addition, it deals with adiabatic and stochastic approximations to unitary ordered exponentials. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics. h. m. f ri ed received his PhD from Stanford University in 1957. He spent a post-doctoral year at the Ecole Normale Sup´erieure in Paris and then three years teaching physics at UCLA. This was followed by a year as a visiting member of the Institute of Advanced Study in Princeton, and two years as a visiting physicist at the Courant Institute at NYU, before joining the Physics Department at Brown University. Professor Fried has lectured and performed research in university departments and institutes throughout the world, principally in Paris, Marseille and Nice, and is a Director of the Workshops on Non-Perturbative QCD, which alternate between the American University of Paris and La Citadelle, Villefranche-sur-Mer. He is now Professor Emeritus of Physics at Brown University and continues to do occasional teaching there, as well as maintaining a research program in theoretical aspects of quantum field theory. This page intentionally left blank GREEN’S FUNCTIONS AND ORDERED EXPONENTIALS H. M. FRIED PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING) FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge CB2 IRP 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia http://www.cambridge.org © Cambridge University Press 2002 This edition © Cambridge University Press (Virtual Publishing) 2003 First published in printed format 2002 A catalogue record for the original printed book is available from the British Library and from the Library of Congress Original ISBN 0 521 44390 3 hardback ISBN 0 511 02062 7 virtual (netLibrary Edition) This book is dedicated to the memory of three extraordinary Physicists and Human Beings, men who died during the ten-year period of the writing of this book. From these Scholars and Gentlemen the author was privileged to learn a little of both Physics and the Humanity which can coexist in even the greatest of scientists: Profs. Donald Yennie, Antoine Visconti, and Julian Schwinger. This page intentionally left blank Contents 1 2