Functional determinants for general Sturm-Liouville problems

Klaus Kirsten, Alan J. McKane

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Simple and analytically tractable expressions for functional determinants are known to exist for many cases of interest. We extend the range of situations for which these hold to cover systems of self-adjoint operators of the Sturm-Liouville type with arbitrary linear boundary conditions. The results hold whether or not the operators have negative eigenvalues. The physically important case of functional determinants of operators with a zero mode, but where that mode has been extracted, is studied in detail for the same range of situations as when no zero mode exists. The method of proof uses the properties of generalized zeta-functions. The general form of the final results is the same for the entire range of problems considered.
    Original languageEnglish
    Pages (from-to)4649-4670
    Number of pages21
    JournalJournal of Physics A: Mathematical and General
    Volume37
    Issue number16
    DOIs
    Publication statusPublished - 23 Apr 2004

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