One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly

Details One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly One-loop Effective Potential for a Fixed Charged Self-interacting Bosonic Model at Finite Temperature with its Related Multiplicative Anomaly

1997-10-22

arxiv.org/abs/hep-th/9710171v2

Phys.Rev. D57 (1998) 7430-7443

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, RevTex, a new Section and several explanations added concering the non-commutative residue and the physical discussi

Scientific paper

10.1103/PhysRevD.57.7430

The one-loop partition function for a charged self-interacting Bose gas 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 treatments and coming from the multiplicative anomaly related to functional determinants-- is found and its dependence on the mass and chemical potential is obtained. The presence of the new term is shown to be crucial for having the factorization invariance of the regularized partition function. In the non interacting case, the relativistic Bose-Einstein condensation is revisited. By means of a suitable charge renormalization, for D=4 the symmetry breaking phase is shown to be unaffected by the new term, which, however, gives actually rise to a non vanishing new contribution in the unbroken phase.

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