Renormalized thermal entropy in field theory

Author(s): S. L. Cacciatori, F. M. Costa, F. Piazza

Journal: Phys. Rev. D

Volume: 79

Page(s): 025006

Year: 2009

DOI Number: 10.1103/PhysRevD.79.025006

Link: Link to publication


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 þ 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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