Ten Physical Applications of Spectral Zeta Functions

Ten Physical Applications of Spectral Zeta Functions
Title Ten Physical Applications of Spectral Zeta Functions PDF eBook
Author Emilio Elizalde
Publisher Springer Science & Business Media
Pages 229
Release 2008-12-04
Genre Science
ISBN 3540447571

Download Ten Physical Applications of Spectral Zeta Functions Book in PDF, Epub and Kindle

This monography is, in the first place, a commented guide that invites the reader to plunge into the thrilling world ofzeta functions and their appli cations in physics. Different aspects ofthis field ofknowledge are considered, as one can see specifically in the Table of Contents. The level of the book is elementary. It is intended for people with no or little knowledge of the subject. Everything is explained in full detail, in particular, the mathematical difficulties and tricky points, which too often constitute an insurmountable barrier for those who would have liked to be come aquainted with that matter but never dared to ask (or did not manage to understand more complete, higher-level treatises). In this sense the present work is to be considered as a basic introduction and exercise collection for other books that have appeared recently. Concerning the physical applications of the method ofzeta-function reg ularization here described, quite a big choice is presented. The reader must be warned, however, that I have not tried to explain the underlying physi cal theories in complete detail (since this is undoubtedly out of scope), but rather to illustrate - simply and clearly - the precise way the method must be applied. Sometimes zeta regularization is explicitly compared in the text with other procedures the reader is supposed to be more familiar with (such as cut-off or dimensional regularization).

Ten Physical Applications of Spectral Zeta Functions

Ten Physical Applications of Spectral Zeta Functions
Title Ten Physical Applications of Spectral Zeta Functions PDF eBook
Author Emilio Elizalde
Publisher Springer
Pages 234
Release 2012-05-31
Genre Science
ISBN 3642294057

Download Ten Physical Applications of Spectral Zeta Functions Book in PDF, Epub and Kindle

Zeta-function regularization is a powerful method in perturbation theory, and this book is a comprehensive guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice, for example in the Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, and non-commutative spacetime. The formulae, some of which are new, can be directly applied in creating physically meaningful, accurate numerical calculations. The book acts both as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice. Thoroughly revised, updated and expanded, this new edition includes novel, explicit formulas on the general quadratic, the Chowla-Selberg series case, an interplay with the Hadamard calculus, and also features a fresh chapter on recent cosmological applications, including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.

Zeta Regularization Techniques with Applications

Zeta Regularization Techniques with Applications
Title Zeta Regularization Techniques with Applications PDF eBook
Author E. Elizalde
Publisher World Scientific
Pages 344
Release 1994
Genre Science
ISBN 9789810214418

Download Zeta Regularization Techniques with Applications Book in PDF, Epub and Kindle

This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.

Zeta Regularization Techniques With Applications

Zeta Regularization Techniques With Applications
Title Zeta Regularization Techniques With Applications PDF eBook
Author Andrei A Bytsenko
Publisher World Scientific
Pages 336
Release 1994-05-16
Genre Science
ISBN 9814502987

Download Zeta Regularization Techniques With Applications Book in PDF, Epub and Kindle

This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.

Spectral Functions in Mathematics and Physics

Spectral Functions in Mathematics and Physics
Title Spectral Functions in Mathematics and Physics PDF eBook
Author Klaus Kirsten
Publisher CRC Press
Pages 207
Release 2001-12-13
Genre Mathematics
ISBN 1000738159

Download Spectral Functions in Mathematics and Physics Book in PDF, Epub and Kindle

The literature on the spectral analysis of second order elliptic differential operators contains a great deal of information on the spectral functions for explicitly known spectra. The same is not true, however, for situations where the spectra are not explicitly known. Over the last several years, the author and his colleagues have developed new,

A Window Into Zeta and Modular Physics

A Window Into Zeta and Modular Physics
Title A Window Into Zeta and Modular Physics PDF eBook
Author Klaus Kirsten
Publisher Cambridge University Press
Pages 361
Release 2010-05-24
Genre Mathematics
ISBN 0521199301

Download A Window Into Zeta and Modular Physics Book in PDF, Epub and Kindle

Consists of lectures that are part of the MSRI workshops and that introduce students and researchers to the intriguing world of theoretical physics.

Cosmology, Quantum Vacuum and Zeta Functions

Cosmology, Quantum Vacuum and Zeta Functions
Title Cosmology, Quantum Vacuum and Zeta Functions PDF eBook
Author Sergey D. Odintsov
Publisher Springer Science & Business Media
Pages 379
Release 2011-06-10
Genre Science
ISBN 3642197604

Download Cosmology, Quantum Vacuum and Zeta Functions Book in PDF, Epub and Kindle

Some major developments of physics in the last three decades are addressed by highly qualified specialists in different specific fields. They include renormalization problems in QFT, vacuum energy fluctuations and the Casimir effect in different configurations, and a wealth of applications. A number of closely related issues are also considered. The cosmological applications of these theories play a crucial role and are at the very heart of the book; in particular, the possibility to explain in a unified way the whole history of the evolution of the Universe: from primordial inflation to the present day accelerated expansion. Further, a description of the mathematical background underlying many of the physical theories considered above is provided. This includes the uses of zeta functions in physics, as in the regularization problems in QFT already mentioned, specifically in curved space-time, and in Casimir problems as.