論文の公開元へNonanalytic term in the effective potential at finite temperature for a scalar field on compactified space
概要
We study nonanalytic terms, which cannot be written in the form of any positive integer power of fielddependent mass squared, in effective potential at finite temperature in one-loop approximation for a real scalar field on the D-dimensional spacetime, S1 τ × RD−ðpþ1Þ × Qp i¼1 S1 i . The effective potential can be recast into the integral form in the complex plane by using the integral representation for the modified Bessel function of the second kind and the analytical extension for multiple mode summations. The pole structure of the mode summations is clarified and all the nonanalytic terms are obtained by the residue theorem. We find that the effective potential has a nonanalytic term when the dimension of the flat Euclidean space, D − ðp þ 1Þ is odd. There appears only one nonanalytic term for the given values of D and p, for which the nonanalytic term exists.
