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© 2011

Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory

Book

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

    1. Front Matter
      Pages 219-219
    2. Dmitri Fursaev, Dmitri Vassilevich
      Pages 221-271
  6. 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

  1. 1.Dubna International UniversityDubnaRussian Federation
  2. 2.CMCCUniversidade Federal do ABCSanto AndreBrazil

About the authors

The authors D. Vassilevich and D. Fursaev are acknowledged experts in spectral geometry and quantum gravity. D. Fursaev has published more than 60 articles in high profile science journals, and he was appointed the rector of Dubna International University in 2008. D. Vassilevich is a professor for mathematical physics at the Universidade Federal do ABC, Santo Andre (Brazil). He published more than 100 articles in scientific journals and is author of the book "”Fundamental Interactions - A Memorial Volume for Wolfgang Kummer" (2009).

Bibliographic information

Industry Sectors
Energy, Utilities & Environment

Reviews

From the reviews:

“The authors have tried to make the book as self-contained as possible with the declared purpose that it should be useful for both active researchers and graduate students. The inclusion in the book of more than a hundred exercises with their solutions makes it indeed possible to use the material in it for lecture courses on physical applications of the spectral theory. … This is a good book, unique in several ways, clearly written … and also a very useful reference for practical purposes.” (Emili Elizalde, Mathematical Reviews, Issue 2012 f)

“This book represents an introduction into the theory of spectral functions and their applications to quantum field theory (QFT). … more than a hundred exercises with their solutions help the reader to understand better the topic and makes possible the use of this book in lecture courses on physical applications of the spectral theory. … Noncommutative theories are a beautiful example of how physics and mathematics have a mutual influence. Each chapter contains exercises, which are integer part of the book.” (Marian Ioan Munteanu, Zentralblatt MATH, Vol. 1230, 2012)