Lecture Notes in Physics

Ten Physical Applications of Spectral Zeta Functions

Authors: Elizalde, Emilio

  • Authored by a leading expert in the field
  • Tutorial and self-contained presentation
  • Contains both theory and applications
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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)

  • Introduction and Outlook

    Elizalde, Emilio

    Pages 1-22

  • Mathematical Formulas Involving the Different Zeta Functions

    Elizalde, Emilio

    Pages 23-48

  • A Treatment of the Non-polynomial Contributions: Application to Calculate Partition Functions of Strings and Membranes

    Elizalde, Emilio

    Pages 49-66

  • Analytical and Numerical Study of Inhomogeneous Epstein and Epstein–Hurwitz Zeta Functions

    Elizalde, Emilio

    Pages 67-93

  • Physical Application: The Casimir Effect

    Elizalde, Emilio

    Pages 95-118

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-29405-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-29404-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Ten Physical Applications of Spectral Zeta Functions
Authors
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 and Tables
14 b/w illustrations
Topics