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arXiv · hep-th/0601084

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

Guido Cognola·Emilio Elizalde·Sergio Zerbini
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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.

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Guido Cognola, Emilio Elizalde, Sergio Zerbini. 2006-06-29. Heat-kernel expansion on non compact domains and a generalised zeta-function regularisation procedure. https://doi.org/10.1063/1.2259580

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