Thermal Bosonic and Fermionic Quantum Fields in Static Background Gauge Potentials

TL;DR

This paper analyzes the finite-temperature energy-momentum tensor of scalar and spinor fields in static electromagnetic backgrounds, revealing distinct behaviors of virtual sea and thermal plasma components, including periodicity effects.

Contribution

It provides a detailed study of the energy-momentum tensor in static background gauge fields at finite temperature, highlighting the separation into UV divergent and finite parts and their different responses to electric and magnetic fields.

Findings

The virtual sea component remains uniform under a uniform electric field.

The thermal plasma component exhibits a periodic structure with period 2πT/E.

Periodic behavior also occurs for magnetic fields with compactified spatial directions.

Abstract

We study at finite temperature the energy-momentum tensor $T_{\mu\nu}(x)$ of (i) a scalar field in arbitrary dimension, and (ii) a spinor field in 1+1 dimensions, interacting with a static background electromagnetic field. $T_{\mu\nu}$ separates into an UV divergent part $T_{\mu\nu}^{sea}$ representing the virtual sea, and an UV finite part $T_{\mu\nu}^{plasma}$ describing the thermal plasma of the matter field. $T_{\mu\nu}^{sea}$ remains uniform in the presence of a \underbar{uniform} electric field $\vec E$, while $T_{\mu\nu}^{plasma}$ becomes a periodic function with period $\Delta x=2\pi T/E$ in the direction parallel to $\vec E$. A related periodicity is found for a uniform static magnetic field if one spatial direction perpendicular to the magnetic field is compactified to a circle.