Spectral zeta functions for a cylinder and a circle

Spectral zeta functions ζ(s) for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis −1⩽ Re...

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Bibliographic Details
Published in:Journal of mathematical physics 2000-07, Vol.41 (7), p.4521-4531
Main Authors: Nesterenko, V. V., Pirozhenko, I. G.
Format: Article
Language:English
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Summary:Spectral zeta functions ζ(s) for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis −1⩽ Re  s⩽0. Proceeding from this the spectral zeta functions for the boundary conditions given on a circle (boundary value problem on a plane) are obtained without any additional calculations. The Casimir energy for the relevant field configurations is deduced.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.533358