Fermionic functional integrals and the renormalization group / Joel Feldman, Horst Knorrer, Eugene Trubowitz.

Format:

Book

Author/Creator:

Feldman, Joel S., 1949- author.

Knörrer, Horst, author.

Trubowitz, Eugene, author.

Series:

CRM monograph series ; Volume 16.

CRM Monograph Series ; Volume 16

Language:

English

Subjects (All):

Integration, Functional.

Renormalization group.

Mathematical physics.

Physical Description:

1 online resource (118 pages) : illustrations.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2002.

Summary:

This book, written by well-known experts in the field, offers a concise summary of one of the latest and most significant developments in the theoretical analysis of quantum field theory. The renormalization group is the name given to a technique for analyzing the qualitative behavior of a class of physical systems by iterating a map on the vector space of interactions for the class. In a typical nonrigorous application of this technique, one assumes, based on one's physicalintuition, that only a certain finite dimensional subspace (usually of dimension three or less) is important. The material in this book concerns a technique for justifying this approximation in a broad class of fermionic models used in condensed matter and high energy physics. This volume is based on theAisenstadt Lectures given by Joel Feldman at the Centre de Recherches Mathematiques (Montreal, Canada). It is suitable for graduate students and research mathematicians interested in mathematical physics. Included are many problems and solutions.

Contents:

Machine generated contents note: Chapter 1. Fermionic Functional Integrals

1.1. Grassmann Algebras

1.2. Grassmann Integrals

1.3. Differentiation and Integration by Parts

1.4. Grassmann Gaussian Integrals

1.5. Grassmann Integrals and Fermionic Quantum Field Theories

1.6. The Renormalization Group

1.7. Wick Ordering

1.8. Bounds on Grassmann Gaussian Integrals

Chapter 2. Fermionic Expansions

2.1. Notation and Definitions

2.2. The Expansion-Algebra

2.3. The Expansion-Bounds

2.4. Sample Applications

Appendix A. Infinite-Dimensional Grassmann Algebras

Appendix B. Pfaffians

Appendix C. Propagator Bounds

Appendix D. Problem Solutions

Chapter 1. Fermionic Functional Integrals

Appendix C. Propagator Bounds.

Notes:

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-3861-5