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Springer Tracts in Modern Physics Vol.211--Evaluating Feynman integrals 2004
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Preface The goal of this book is to describe in detail how Feynman integrals1 can be evaluated analytically. The problem of evaluating Lorentz-covariant Feynman integrals over loop momenta originated in the early days of perturbative quantum field theory. Over a span of more than fifty years, a great variety of methods for evaluating Feynman integrals has been developed. This book is a first attempt to summarize them. I understand that if another person – in particular one actively involved in developing methods for Feynman integral evaluation – made a similar attempt, he or she would probably concentrate on some other methods and would rank the methods as most important and less important in a different order. I believe, however, that my choice is reasonable. At least I have tried to concentrate on the methods that have been used in the past few years in the most sophisticated calculations, in which world records in the Feynman integral ‘sport’ were achieved. The problem of evaluation is very important at the moment. What could be easily evaluated was evaluated many years ago. To perform important calculations at the two-loop level and higher one needs to choose adequate methods and combine them in a non-trivial way. In the present situation – which might be considered boring because the Standard Model works more or less properly and there are no glaring contradictions with experiment – one needs not only to organize new experiments but also perform rather non- trivial calculations for further crucial high-precision checks. So I hope very much that this book will be used as a textbook in practical calculations. I shall concentrate on analytical methods and only briefly describe nu- merical ones. Some methods are also characterized as semi-analytical, for example, the method based on asymptotic expansions of Feynman integrals in momenta and masses which was described in detail in my previous book. In this method, it is also necessary to apply some analytical methods of eval- uation which were described there only very briefly. So the present book can be considered as Volume 1 with respect to the previous book, which might be termed Volume 2, or the sequel. Although all the necessary definitions concerning Feynman integrals are provided in the book, it would be helpful for the reader to know the basics of perturbative quantum field theory, e.g. by following the first few chapters of the well-known textbooks by Bogoliubov and Shirkov and/or Peskin and Schroeder. This book is based on the course of lectures which I gave in the winter semester of 2003–2004 at the Universities of Hamburg and Karlsruhe as a DFG Mercator professor in Hamburg. It is my pleasure to thank the students, postgraduate students, postdoctoral fellows and professors who attended my lectures for numerous stimulating discussions. I am grateful very much to B. Feucht, A.G. Grozin and J. Piclum for careful reading of preliminary versions of the whole book and numerous com- ments and suggestions; to M. Czakon, M. Kalmykov, P. Mastrolia, J. Piclum, M. Steinhauser and O.L. Veretin for valuable assistance in presenting exam- ples in the book; to C. Anastasiou, K.G. Chetyrkin and A.I. Davydychev for various instructive discussions; to P.A. Baikov, M. Beneke, K.G. Chetyrkin, A. Czarnecki, A.I. Davydychev, B. Feucht, G. Heinrich, A.A. Penin, A. Signer, M. Steinhauser and O.L. Veretin for fruitful collaboration on evaluating Feynman integrals; to M. Czakon, A. Czarnecki, T. Gehrmann, J. Gluza, T. Riemann, K. Melnikov, E. Remiddi and J.B. Tausk for stimulating com- petition; to Z. Bern, L. Dixon, C. Greub and S. Moch for various pieces of advice; and to B.A. Kniehl and J.H. K¨uhn for permanent support. I am thankful to my family for permanent love, sympathy, patience and understanding. Moscow – Hamburg, V.A. Smirnov October 2004 Download link：http://www.isload.com.cn/store/vrdhmiev2tds6 [ Last edited by zhq025 on 2008-1-16 at 10:38 ] |
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