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The Hadamard parametrix is a representation of the short-distance singularitystructure of the Feynman Green's function for a quantum field on a curvedspace-time background. Subtracting these divergent terms regularizes theFeynman Green's function and enables the computation of renormalizedexpectation values of observables. We study the Hadamard parametrix for acharged, massive, complex scalar field in five space-time dimensions. Even inMinkowski space-time, it is not possible to write the Feynman Green's functionfor a charged scalar field exactly in closed form. We therefore presentcovariant Taylor series expansions for the biscalars arising in the Hadamardparametrix. On a general space-time background, we explicitly state theexpansion coefficients up to the order required for the computation of therenormalized scalar field current. These coefficients become increasinglylengthy as the order of the expansion increases, so we give the higher-orderterms required for the calculation of the renormalized stress-energy tensor inMinkowski space-time only.

Hadamard parametrix of the Feynman Green's function of a five-dimensional charged scalar field