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MiS Preprint

Functional determinants by contour integration methods

Klaus Kirsten and Alan J. McKane


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.

MSC Codes:
58C40, 58J50
functional determinants, sturm-liouville problems, contour integrations

Related publications

2003 Repository Open Access
Klaus Kirsten and Alan J. McKane

Functional determinants by contour integration methods

In: Annals of physics, 308 (2003) 2, pp. 502-527