Zero-point energies and the multiplicative anomaly

Details Zero-point energies and the multiplicative anomaly Zero-point energies and the multiplicative anomaly

2000-05-22

arxiv.org/abs/hep-th/0005201v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, REVTeX, no figures. Submitted to Physical Review D

Scientific paper

For the case of a relativistic scalar field at finite temperature with a chemical potential, we calculate an exact expression for the one-loop effective action using the full fourth order determinant and zeta-function regularisation. We find that it agrees with the exact expression for the factored operator and thus there appears to be no mulitplicative anomaly. The appearance of the anomaly for the fourth order operator in the high temperature limit is explained and we show that the multiplicative anomaly can be calculated as the difference between two zeta-regularised zero-point energies. This difference is a result of using a charge operator in the Hamiltonian which has not been normal ordered.

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