- Authored by a leading expert in the field
- Tutorial and self-contained presentation
- Contains both theory and applications
Buy this book
- About this book
-
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.
- About the authors
-
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.
- Table of contents (10 chapters)
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Introduction and Outlook
Pages 1-22
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Mathematical Formulas Involving the Different Zeta Functions
Pages 23-48
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A Treatment of the Non-polynomial Contributions: Application to Calculate Partition Functions of Strings and Membranes
Pages 49-66
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Analytical and Numerical Study of Inhomogeneous Epstein and Epstein–Hurwitz Zeta Functions
Pages 67-93
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Physical Application: The Casimir Effect
Pages 95-118
-
Table of contents (10 chapters)
- Download Preface 1 PDF (48.4 KB)
- Download Sample pages 2 PDF (329.1 KB)
- Download Table of contents PDF (114.5 KB)
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Bibliographic Information
- Bibliographic Information
-
- Book Title
- Ten Physical Applications of Spectral Zeta Functions
- Authors
-
- Emilio Elizalde
- Series Title
- Lecture Notes in Physics
- Series Volume
- 855
- Copyright
- 2012
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-29405-1
- DOI
- 10.1007/978-3-642-29405-1
- Softcover ISBN
- 978-3-642-29404-4
- Series ISSN
- 0075-8450
- Edition Number
- 2
- Number of Pages
- XIV, 227
- Number of Illustrations
- 14 b/w illustrations
- Topics
