A statistical approach to quantum field theory : an introduction / Andreas Wipf.

Format:

Book

Author/Creator:

Wipf, Andreas.

Series:

Lecture notes in physics ; 864.

Lecture notes in physics, 0075-8450 ; v. 864

Language:

English

Subjects (All):

Quantum field theory--Mathematics.

Quantum field theory.

Field theory (Physics).

Physical Description:

1 online resource (XVIII, 390 p. 133 illus.)

Edition:

1st ed. 2013.

Place of Publication:

Heidelberg ; New York : Springer Verlag, c2013.

Language Note:

English

Summary:

Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures. Accordingly, the first chapters of this book contain a self-contained introduction to path integrals in Euclidean quantum mechanics and statistical mechanics. The resulting high-dimensional integrals can be estimated with the help of Monte Carlo simulations based on Markov processes. The most commonly used algorithms are presented in detail so as to prepare the reader for the use of high-performance computers as an “experimental” tool for this burgeoning field of theoretical physics. Several chapters are then devoted to an introduction to simple lattice field theories and a variety of spin systems with discrete and continuous spins, where the ubiquitous Ising model serves as an ideal guide for introducing the fascinating area of phase transitions. As an alternative to the lattice formulation of quantum field theories, variants of the flexible renormalization group methods are discussed in detail. Since, according to our present-day knowledge, all fundamental interactions in nature are described by gauge theories, the remaining chapters of the book deal with gauge theories without and with matter. This text is based on course-tested notes for graduate students and, as such, its style is essentially pedagogical, requiring only some basics of mathematics, statistical physics, and quantum field theory. Yet it also contains some more sophisticated concepts which may be useful to researchers in the field. Each chapter ends with a number of problems – guiding the reader to a deeper understanding of some of the material presented in the main text – and, in most cases, also features some listings of short, useful computer programs.

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

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

3-642-33105-X