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.
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).
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)