Heat-kernel expansion on noncompact domains and a generalized zeta-function regularization procedure

Guido Cognola, Emilio Elizalde, Sergio Zerbini

    Research output: Contribution to journalArticleResearchpeer-review

    12 Citations (Scopus)

    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 languageEnglish
    Article number083516
    JournalJournal of Mathematical Physics
    Volume47
    Issue number8
    DOIs
    Publication statusPublished - 11 Sep 2006

    Fingerprint Dive into the research topics of 'Heat-kernel expansion on noncompact domains and a generalized zeta-function regularization procedure'. Together they form a unique fingerprint.

    Cite this