

Preprint 57/2003
Functional determinants by contour integration methods
Klaus Kirsten and Alan J. McKane
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Submission date: 08. Jul. 2003
Pages: 31
published in: Annals of physics, 308 (2003) 2, p. 502-527
DOI number (of the published article): 10.1016/S0003-4916(03)00149-0
Bibtex
MSC-Numbers: 58C40, 58J50
PACS-Numbers: 02.30.-f
Keywords and phrases: functional determinants, sturm-liouville problems, contour integrations
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Abstract:
We present a simple and accessible method which uses contour
integration methods to derive formulae for functional
determinants. To make the presentation as clear as possible, the
general idea is first illustrated on the simplest case: a second
order differential operator with Dirichlet boundary conditions.
The method is applicable to more general situations, and we
discuss the way in which the formalism has to be developed to
cover these cases. In particular, we also show that simple and
elegant formulae exist for the physically important case of
determinants where zero modes exist, but have been excluded.