Zeta function regularization in de Sitter space: the Minkowski limit

Abstract

We study an integral representation for the zeta function of the one-loop effective potential for a minimally coupled massive scalar field in D-dimensional de Sitter spacetime. By deforming the contour of integration we present it in a form suitable for letting the de Sitter radius tend to infinity, and we demonstrate explicitly for the case D=2 that the quantities $\zeta( 0 )$ and $\zeta'( 0 )$ have the appropriate Minkowski limits.