A window into zeta and modular physics / edited by Klaus Kirsten, Floyd L. Williams.

Format:

Book

Contributor:

Kirsten, Klaus, 1962-

Williams, Floyd L.

Series:

Mathematical Sciences Research Institute publications ; 57.

Mathematical Sciences Research Institute publications ; 57

Language:

English

Subjects (All):

Functions, Zeta--Congresses.

Functions, Zeta.

Forms, Modular--Congresses.

Forms, Modular.

Mathematical physics--Congresses.

Mathematical physics.

Genre:

Conference papers and proceedings.

Physical Description:

351 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge ; New York : Cambridge University Press, 2010.

Summary:

"A book consisting of lectures that are part of the series of MSRI workshops and that introduce students and researchers to a portion of the intriguing world of theoretical physics"-- Provided by publisher.

"This book provides an introduction to (1) various zeta functions (for example, Riemann, Hurwitz, Barnes, Epstein, Selberg, and Ruelle), including graph zeta functions; (2) modular forms (Eisenstein series, Hecke and Dirichlet L-functions, Ramanujan's tau function, and cusp forms); and (3) vertex operator algebras (correlation functions, quasimodular forms, modular invariance, rationality, and some current research topics including higher genus conformal field theory). Various concrete applications of the material to physics are presented. These include Kaluza-Klein extra dimensional gravity, Bosonic string calculations, an abstract Cardy formula for black hole entropy, Patterson-Selberg zeta function expression of one-loop quantum field and gravity partition functions, Casimir energy calculations, atomic Schrödinger operators, Bose-Einstein condensation, heat kernel asymptotics, random matrices, quantum chaos, elliptic and theta function solutions of Einstein's equations, a soliton-black hole connection in two-dimensional gravity, and conformal field theory"-- Provided by publisher.

Contents:

Part I. Introductory Lectures: 1. Lectures on zeta functions, L-functions and modular forms with some physical applications / Floyd L. Williams

2. Basic zeta functions and some applications in physics / Klaus Kirsten

3. Zeta functions and chaos Audrey Terras

4. Vertex operators and modular forms / Geoffrey Mason and Michael Tuite

Part II. Research Lectures: 5. Applications of elliptic and theta functions to Friedmann-Robertson-Lemaıtre-Walker cosmology with cosmological constant / Jennie D'Ambroise

6. Integrable systems and 2D gravitation: How a soliton illuminates a black hole / Shabnam Beheshti

7. Functional determinants in higher dimensions using contour integrals / Klaus Kirsten

8. The role of the Patterson-Selberg zeta function of a hyperbolic cylinder in three-dimensional gravity with a negative cosmological constant / Floyd L. Williams.

Notes:

Includes bibliographical references.

ISBN:

9780521199308

0521199301

OCLC:

573196469

Online:

Cover image