Debye screening in the full electromagnetic thermal model

Determine whether the singular thermal electrostatic contribution in the quadratic free-energy functional for the Pauli–Villars-regularised Dirac field at positive temperature produces a Debye screening effect when both electric and magnetic fields are present.

Background

The paper derives a quadratic term in the Pauli–Villars-regularised free energy that contains the thermal Fourier multiplier $\Gamma(k,\beta)/|k|^2$. The factor $|k|^{-2}$ indicates a possible singularity at zero momentum, unlike the other linear-response contributions.

In the purely electrostatic case, prior work established that the total potential becomes short-range, which is interpreted as Debye screening. The paper conjectures that an analogous screening phenomenon persists when an external magnetic field is also present, but does not establish this in the full electromagnetic setting.