ONE-LOOP EFFECTIVE POTENTIAL FOR A FIXED CHARGED SELF-INTERACTING BOSONIC MODEL AT FINITE-TEMPERATURE WITH ITS RELATED MULTIPLICATIVE ANOMALY

The one-loop partition function for a charged self-interacting Bose ga s at finite temperature in D-dimensional spacetime is evaluated within a path integral approach making use of zeta-function regularization. For D even, a new additional vacuum term-overlooked in all previous tr eatments and coming from the multiplicative anomaly related to functio nal determinants-is found and its dependence on the mass and chemical potential is obtained. The presence of the new term is shown to be cru cial for having the factorization invariance of the regularized partit ion function. In the noninteracting case, the relativistic Bose-Einste in condensation is reexamined. By means of a suitable charge renormali zation, for D=4 the symmetry breaking phase is shown to be unaffected by the new term, which, however, actually gives rise to a nonvanishing new contribution in the unbroken phase.