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Title
Statistical approach to quantum field theory : an introduction / Andreas Wipf.
Edition
Second edition.
ISBN
9783030832636 (electronic bk.)
3030832635 (electronic bk.)
9783030832629
3030832627
Published
Cham : Springer, [2021]
Copyright
©2021
Language
English
Description
1 online resource : illustrations (some color)
Item Number
10.1007/978-3-030-83263-6 doi
Call Number
QC174.45 .W56 2021
Dewey Decimal Classification
530.15
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed November 5, 2021).
Series
Lecture notes in physics ; 992. 1616-6361
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.
