Spectral Zeta Functions for a Cylinder and a Circle

Details Spectral Zeta Functions for a Cylinder and a Circle Spectral Zeta Functions for a Cylinder and a Circle

1999-10-12

arxiv.org/abs/hep-th/9910097v2

J.Math.Phys. 41 (2000) 4521-4531

Physics

High Energy Physics

High Energy Physics - Theory

REVTeX4, 13 pages, no tables and figures; v2 some misprints are corrected

Scientific paper

10.1063/1.533358

Spectral zeta functions $\zeta(s)$ 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 $-1\le$ Re $s \le 0$. 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.

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