Heat-kernel expansion on non compact domains and a generalised zeta-function regularisation procedure

Abstract

Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum in non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several examples. It is pointed out that for a class of exponential (analytic) interactions, generically the non-compactness of the domain gives rise to logarithmic terms in the heat-kernel expansion. Then, a meromorphic continuation of the associated zeta function is investigated. A simple model is considered, for which the analytic continuation of the zeta function is not regular at the origin, displaying a pole of higher order. For a physically meaningful evaluation of the related functional determinant, a generalised zeta function regularisation procedure is proposed.

Latex, 14 pages, no figures. The version to be published in JMP

References in corpus (3)

• Spectral analysis of a flat plasma sheet model
• The very unusual properties of the resolvent, heat kernel, and zeta function for the operator $-d^2/d{r}^2-1/(4r^2)$
• Zeta-function approach to Casimir energy with singular potentials

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