# Ten Physical Applications of Spectral Zeta Functions

Part of the Lecture Notes in Physics book series (LNP, volume 855)

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Part of the Lecture Notes in Physics book series (LNP, volume 855)

Zeta-function regularization is a powerful method in perturbation theory.

This book is meant as a 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 (e.g. Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, noncommutative spacetime). The formulas some of which are new can be used for physically meaningful, accurate numerical calculations. The book is to be considered as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice.

This thoroughly revised, updated and expanded edition includes in particular new explicit formulas on the general quadratic, Chowla-Selberg series case, an interplay with the Hadamard calculus, and features a new chapter on recent cosmological applications including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.

Casimir physics Elliptic partial differential operators Regularization and renormalization Spectral zeta functions Vaccum energy fluctuations

- DOI https://doi.org/10.1007/978-3-642-29405-1
- Copyright Information Springer-Verlag Berlin Heidelberg 2012
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-642-29404-4
- Online ISBN 978-3-642-29405-1
- Series Print ISSN 0075-8450
- Series Online ISSN 1616-6361
- Buy this book on publisher's site

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