Renormalized Thermal Entropy in Field Theory

TL;DR

This paper introduces a renormalized entropy in quantum field theory based on Newton-Wigner localization, eliminating divergences and ensuring consistent thermodynamic behavior for subsystems.

Contribution

It proposes a new definition of entropy using Newton-Wigner localization that removes UV divergences in quantum field theory calculations.

Findings

Renormalized entropy is divergence-free and thermodynamically consistent.

At high temperatures, results match standard QFT after subtracting divergences.

Entropy approaches zero at low temperatures with a different temperature dependence.

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.