Statistical Approach to Quantum Field Theory: An Introduction

by Andreas Wipf

Overview

This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.

Product Details

ISBN-13:	9783030832629
Publisher:	Springer International Publishing
Publication date:	10/27/2021
Series:	Lecture Notes in Physics , #992
Edition description:	2nd ed. 2021
Pages:	554
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Andreas Wipf is full professor at the Friedrich-Schiller-University (FSU) of Jena, Germany, where he teaches many courses related to theoretical physics. His research focuses on quantum field theory in the continuum and on lattice, structural aspects of quantum theory, quantum systems under extreme conditions, conformal and supersymmetric field theories, and the role of symmetries and symmetry breaking in theoretical physics. He obtained his Diploma at the Department of Physics at ETH Zurich, and his Ph.D. at the Institute for Theoretical Physics of the University of Zurich. He covered positions as postdoctoral fellow, assistant professor, and Privatdozent at the Dublin Institute for Advanced Studies, Los Alamos National Laboratory, Max-Planck-Institute for Physics (Werner-Heisenberg-Institute) in Munich, and at ETH Zurich where he habilitated in 1995. Then, he moved to Jena as full professor and has been Director of the Institute for Theoretical Physics, Dean of the Physics and Astronomy Faculty, Spokesman of the research training group on gravity, quantum field theory, and mathematical physics. He co-authored the textbooks “Theoretische Physik” (Springer Spektrum, 2015), which presents all theoretical physics up to the bachelor's degree and beyond, and “Theoretische Physik 3 | Quantenmechanik” (Springer Spektrum, 2018).

Table of Contents

Introduction.- Path Integrals in Quantum and Statistical Mechanics.- High-Dimensional Integrals.- Monte Carlo Simulations in Quantum Mechanics.- Scalar Fields at Zero and Finite Temperature.- Classical Spin Models: An Introduction.- Mean Field Approximation.- Transfer Matrices, Correlation Inequalities and Roots of Partition Functions.- High-Temperature and Low-Temperature Expansions.- Peierls Argument and Duality Transformations.- Renormalization Group on the Lattice.- Functional Renormalization Group.- Lattice Gauge Theories.- Two-Dimensional Lattice Gauge Theories and Group Integrals.- Fermions on a Lattice.- Finite Temperature Schwinger Model.- Interacting fermions.

Editorial Reviews

From the reviews:

“This book fills a gap in the literature on non-pertubative aspects of field theories and numerical methods such as Monte Carlo which are usually covered only separately in different books. Providing a new perspective on statistical and quantum field theories, this book is useful for graduate students and researchers within and outside the field. … This book will definitely be a must-read for people who are active in the fields of statistical and quantum field theories.” (Mohammad R. Rahimi Tabar, Mathematical Reviews, October, 2013)

“The book is well written, and pedagogically well-organized. The book has benefited by last-year undergraduate and beginning postgraduate students in physics and applied mathematics. … it also could be useful for researcher in the fields Note that each chapter ends with some problems which help to better understand the material given.” (Farruh Mukhamedov, zbMATH, Vol. 1268, 2013)

From the Publisher