Pseudo-gauge dependence of quantum fluctuations of energy in a hot relativistic gas of fermions

TL;DR

This paper investigates how the calculated quantum fluctuations of energy in a hot relativistic fermionic gas depend on the pseudo-gauge choice of the energy-momentum tensor, showing convergence for large subsystems.

Contribution

It provides explicit formulas for quantum energy fluctuations in a relativistic fermionic gas and demonstrates their pseudo-gauge dependence, clarifying the scale at which gauge choices become irrelevant.

Findings

Quantum fluctuations depend on pseudo-gauge choice for small systems.

Results converge to canonical-ensemble predictions for large subsystems.

Identifies a coarse-graining scale where pseudo-gauge dependence vanishes.

Abstract

Explicit expressions for quantum fluctuations of energy in subsystems of a hot relativistic gas of spin-$1/2$ particles are derived. The results depend on the form of the energy-momentum tensor used in the calculations, which is a feature described as pseudo-gauge dependence. However, for sufficiently large subsystems the results obtained in different pseudo-gauges converge and agree with the canonical-ensemble formula known from statistical physics. As different forms of the energy-momentum tensor of a gas are a priori equivalent, our finding suggests that the concept of quantum fluctuations of energy in very small thermodynamic systems is pseudo-gauge dependent. On the practical side, the results of our calculations determine a scale of coarse graining for which the choice of the pseudo-gauge becomes irrelevant.