Heat-kernel expansion on non compact domains and a generalised zeta-function regularisation procedure
نویسندگان
چکیده
Heat-kernel expansion and zeta function regularisation are discussed for Laplace type operators with discrete spectrum on non compact domains. Since a general theory is lacking, the heat-kernel expansion is investigated by means of several examples. Generically, it is pointed out that for a class of exponential (analytic) interactions, 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 the evaluation of the related functional determinant, a generalised zeta function regularisation procedure is proposed. PACS numbers: 02.30.Tb, 02.70.Hm, 04.62.+v
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