Operators, Geometry and Quanta

Methods of Spectral Geometry in Quantum Field Theory

By: Dmitri Fursaev, Dmitri Vassilevich

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Hardcover | 26 June 2011

At a Glance

Hardcover
304 Pages

Dimensions(cm)
22.86 x 15.24 x 1.91

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$149.01

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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). This book addresses advanced graduate students and researchers in mathematical physics 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.

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"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)

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