Abstract
Heat-kernel expansion and zeta function regularization are discussed for Laplace-type operators with discrete spectrum in noncompact 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 noncompactness 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 generalized zeta function regularization procedure is proposed. © 2006 American Institute of Physics.
Original language | English |
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Article number | 083516 |
Journal | Journal of Mathematical Physics |
Volume | 47 |
Issue number | 8 |
DOIs | |
Publication status | Published - 11 Sep 2006 |