Path Integrals in Field Theory

From the reviews: "Mosel's book, described as an introduction, is aimed at graduate students and research workers in particle physics. ... in about 200 pages the reader has the chance to learn in some detail about a most important area of modern physics. The subject is tough but the style is clear and pedagogic, results for the most part being derived explicitly. ... [It] is clearly the work of a man with considerable teaching experience and is recommended as a readable and helpful account of a rather non-trivial subject." (Lewis Ryder, Journal of Physics, Vol. 37(25), 2004) "This book is an introduction to path integral methods in quantum theory. It is divided into three parts devoted correspondingly to nonrelativistic quantum theory, quantum field theory and gauge theory. ... in this book the author has achieved a reasonable compromise between compactness and profoundness. From one side, he avoided many technical details and concentrated on the main points of the path integral method. From the other side, the principal ideas and logical structure of the theory are made clear, contrary to the pragmatic, recipe-like style of the presentation pf path integral methods in many books on quantum field theory. The book is aimed at graduate students and physicists who need a working knowledge of field theory methods for applications in hadron, particle and nuclear physics." (Michael B. Mensky, Zentralblatt MATH, Vol. 1037(12), 2004) "There is no shortage of books on field theory ... but in this book Ulrich Mosel aims to provide a gentler introduction, more accessible to beginning students. In this he is largely successful, the book is a valuable addition to the literature. ... The level of rigour is quite sufficient for the prospective readership. ... The book is clearly written, well laid out and generally student-friendly ... . It will certainly be valuable to students and researchers ... ." (Professor T. W. B. Kibble, Contemporary Physics, Vol. 46 (4), 2005) "This short and concise textbook is intended as a primer on path integral formalism both in classical and quantum field theories ... . It is ideally suited as an intensive one-semester course, delivering the basics needed by readers to follow developments in field theory. ... paves the way for both more rigorous studies in fundamental mathematical issues as well as for applications in hadron, particle and nuclear physics, thus addressing students in mathematical and theoretical physics alike." (Revista Espanola de Fisica, Vol. 17 (6), 2003) "This is an introductory book on path integral methods in field theories, aimed at graduate students and physicists with a working knowledge of field theory and its applications in particle and nuclear physics." (Lewis H. Ryder, Mathematical Reviews, Issue 2006 e)

• 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.