Operators, Geometry and Quanta : Methods of Spectral Geometry in Quantum Field Theory / by Dmitri Fursaev, Dmitri Vassilevich.

Format:

Book

Author/Creator:

Fursaev, Dmitri, Author.

Vassilevich, Dmitri, Author.

Series:

Theoretical and Mathematical Physics, 1864-5879

Language:

English

Subjects (All):

Physics.

Global analysis (Mathematics).

Manifolds (Mathematics).

Quantum field theory.

String models.

Mathematical Methods in Physics.

Global Analysis and Analysis on Manifolds.

Quantum Field Theories, String Theory.

Local Subjects:

Mathematical Methods in Physics.

Global Analysis and Analysis on Manifolds.

Quantum Field Theories, String Theory.

Physical Description:

1 online resource (293 p.)

Edition:

1st ed. 2011.

Place of Publication:

Dordrecht : Springer Netherlands : Imprint: Springer, 2011.

Language Note:

English

Summary:

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). More than hundred exercises together with their solutions are included. This book addresses advanced graduate students and researchers in mathematical physics and in neighbouring areas with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.

Contents:

1 Preface

2 Notation Index I The Basics: 3 Geometrical Background

4 Quantum fields II Spectral geometry: 5 Operators and their spectra

6 Spectral functions

7 Non-linear spectral problems

8 Anomalies and Index Theorem III Applications: 9 Effective action

10 Anomalies in quantum field theories

11 Vacuum energy

12 Open strings and Born-Infeld action

13 Noncommutative geometry and field theory IV Problem solving: 14 Solutions to exercises.

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

94-007-0205-1

OCLC:

743299506