Energy-momentum correlators of fermions at finite temperature and density

TL;DR

This paper investigates how energy-momentum correlators in a relativistic Fermi gas at finite temperature and density depend on the choice of pseudogauge, revealing gauge dependence at small scales and independence at larger scales.

Contribution

It introduces smeared energy-momentum commutators at finite temperature and density, analyzing their pseudogauge dependence and scale behavior in a relativistic quantum Fermi gas.

Findings

Commutators are pseudogauge dependent at small scales.

At large scales or separations, commutators become pseudogauge independent.

The study provides insights into measurement sensitivities in quantum field theories.

Abstract

Equal-time commutators of different components of the energy-momentum tensor at spatially separated points are calculated for a relativistic quantum Fermi gas at finite temperature and density. Different definitions of such components, also known as different pseudogauges, are used and smeared with a Gaussian profile characterized by the width $\sigma$. In this way, we introduce observables that may represent measurements of energy and momentum in a spatial region of size $\sigma$. We find that the obtained commutators are sensitive to the pseudogauge chosen if the probed systems or the spatial separation are small. The pseudogauge dependence is expected as different quantum operators are analyzed in this case. On the other hand, we find that for sufficiently large probed systems or with large separation, the studied commutators are pseudogauge independent.