Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory

  • Dmitri Fursaev
  • Dmitri Vassilevich
Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. The Basics

    1. Front Matter
      Pages 1-1
    2. Dmitri Fursaev, Dmitri Vassilevich
      Pages 3-28
    3. Dmitri Fursaev, Dmitri Vassilevich
      Pages 29-50
  3. Spectral Geometry

    1. Front Matter
      Pages 51-51
  4. Spectral geometry

    1. Dmitri Fursaev, Dmitri Vassilevich
      Pages 53-65
    2. Dmitri Fursaev, Dmitri Vassilevich
      Pages 67-94
    3. Dmitri Fursaev, Dmitri Vassilevich
      Pages 95-114
    4. Dmitri Fursaev, Dmitri Vassilevich
      Pages 115-124
  5. Applications

    1. Front Matter
      Pages 125-125
    2. Dmitri Fursaev, Dmitri Vassilevich
      Pages 127-155
    3. Dmitri Fursaev, Dmitri Vassilevich
      Pages 157-176
    4. Dmitri Fursaev, Dmitri Vassilevich
      Pages 177-196
    5. Dmitri Fursaev, Dmitri Vassilevich
      Pages 197-204
    6. Dmitri Fursaev, Dmitri Vassilevich
      Pages 205-217
  6. Problem Solving

    1. Front Matter
      Pages 219-219
  7. Problem solving

    1. Dmitri Fursaev, Dmitri Vassilevich
      Pages 221-271
  8. Back Matter
    Pages 273-286

About this book

Introduction

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.

Keywords

Non-linear spectral problems Noncommutative geometry field theory Spectral geometry explained Spectral geometry quantum field theory heat kernel introduction spectral functions quantum field theory quantum soliton quantum solitons book spectral function spectral functions applied vacuum energy

Authors and affiliations

  • Dmitri Fursaev
    • 1
  • Dmitri Vassilevich
    • 2
  1. 1.Dubna International UniversityDubnaRussian Federation
  2. 2.CMCCUniversidade Federal do ABCSanto AndreBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-007-0205-9
  • Copyright Information Springer Science+Business Media B.V. 2011
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-94-007-0204-2
  • Online ISBN 978-94-007-0205-9
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887