Renormalized Thermal Entropy in Field Theory

Details Renormalized Thermal Entropy in Field Theory Renormalized Thermal Entropy in Field Theory

2008-03-28

arxiv.org/abs/0803.4087v3

Phys.Rev.D79:025006,2009

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, final version

Scientific paper

10.1103/PhysRevD.79.025006

Standard entropy calculations in quantum field theory, when applied to a subsystem of definite volume, exhibit area-dependent UV divergences that make a thermodynamic interpretation troublesome. In this paper we define a renormalized entropy which is related with the Newton-Wigner position operator. Accordingly, whenever we trace over a region of space, we trace away degrees of freedom that are localized according to Newton-Wigner localization but not in the usual sense. We consider a free scalar field in d+1 spacetime dimensions prepared in a thermal state and we show that our entropy is free of divergences and has a perfectly sound thermodynamic behavior. In the high temperature/big volume limit our results agree with the standard QFT calculations once the divergent contributions are subtracted from the latter. In the limit of low temperature/small volume the entropy goes to zero but with a different dependence on the temperature.

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