Ultraviolet convergence of thermal corrections in the electromagnetic case

Establish whether the thermal contributions to the Pauli–Villars-regularised free energy of the Dirac field in the full electromagnetic case are ultraviolet-convergent and consequently independent of the Pauli–Villars regularisation parameters under the zero-temperature renormalisation scheme.

Background

The paper notes that thermal corrections are ultraviolet-convergent in the purely magnetic case. This permits the corresponding results to be made independent of the Pauli–Villars regulator masses and coefficients through the renormalisation scheme used at zero temperature.

Whether the same ultraviolet convergence and regulator independence hold when an electrostatic potential is included remains unresolved. The paper explicitly identifies this as an open problem for the full electromagnetic model.