基本説明
Concise textbook intended as a primer on path integral formalism both in classical and quantum field theories, although emphasis is on the latter.
Full Description
This is an introductory book to path integral methods in ?eld theories. It is aimed at graduate students and physicists who need a working knowledge of ?eld theory and its methods for applications in hadron, particle and nuclear physics. While teaching ?eld theory courses over the years I have found that many books on ?eld theory present the path integral methods used in only a very recipe-like way. On the other hand, specialized books on path integrals often contain many more details than are actually needed by non-specialists. I hope that this book here ?lls the gap. It provides enough information to actually follow all the arguments necessary for ?eld theoretical developments without, however, elaborating on the method as such and its mathema- cal intricacies. This book is - in a way - a technical companion to Fields, Symmetries, and Quarks by the present author. The reader of this book should have some knowledge of the relativistic equations of motion of 'classical' quantum theory, but no prior knowledge of ?eld theory is assumed. The material in this book can be covered in a o- semester course with 3 hrs/week. It has evolved in many years of teaching this subject. I am grateful to my students for many helpful questions and comments and, in particular, to Frank Froemel for his help in preparing the ?gures in this book.
Contents
I Non-Relativistic Quantum Theory.- 1 The Path Integral in Quantum Theory.- 2 Perturbation Theory.- 3 Generating Functionals.- II Relativistic Quantum Field Theory.- 4 Relativistic Fields.- 5 Path Integrals for Scalar Fields.- 6 Evaluation of Path Integrals.- 7 Transition Rates and Green's Functions.- 8 Green's Functions.- 9 Perturbative ?4 Theory.- 10 Green's Functions for Fermions.- 11 Interacting Fields.- III Gauge Field Theory.- 12 Path Integrals for QED.- 13 Path Integrals for Gauge Fields.- 14 Examples for Gauge Field Theories.- Units and Metric.- A.1 Units.- A.2 Metric and Notation.- Functionals.- B.1 Definition.- B.2 Functional Integration.- B.2.1 Gaussian Integrals.- B.3 Functional Derivatives.- Renormalization Integrals.- Gaussian Grassmann Integration.- References.
