Renormalized thermal entropy in field theory
Abstract
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.
- Publication:
-
Physical Review D
- Pub Date:
- January 2009
- DOI:
- 10.1103/PhysRevD.79.025006
- arXiv:
- arXiv:0803.4087
- Bibcode:
- 2009PhRvD..79b5006C
- Keywords:
-
- 11.10.-z;
- 03.70.+k;
- 05.30.-d;
- Field theory;
- Theory of quantized fields;
- Quantum statistical mechanics;
- High Energy Physics - Theory;
- General Relativity and Quantum Cosmology;
- Quantum Physics
- E-Print:
- 27 pages, final version