Theoretical and Mathematical Physics

Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory

Authors: Fursaev, Dmitri, Vassilevich, Dmitri

  • Bridges the physical applications of heat kernel theories with the mathematical foundations

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  • ISBN 978-94-007-0205-9
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  • ISBN 978-94-007-0204-2
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Softcover $119.00
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  • ISBN 978-94-007-3663-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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About this book

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.

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).

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)


Table of contents (12 chapters)

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-94-007-0205-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-94-007-0204-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-94-007-3663-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Operators, Geometry and Quanta
Book Subtitle
Methods of Spectral Geometry in Quantum Field Theory
Authors
Series Title
Theoretical and Mathematical Physics
Copyright
2011
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-94-007-0205-9
DOI
10.1007/978-94-007-0205-9
Hardcover ISBN
978-94-007-0204-2
Softcover ISBN
978-94-007-3663-4
Series ISSN
1864-5879
Edition Number
1
Number of Pages
XVI, 288
Additional Information
330 p., 5 images, 1st edition
Topics