High-temperature expansion of the grand thermodynamic potential for scalar particles in crossed electromagnetic fields

TL;DR

This paper derives the high-temperature expansion of the grand thermodynamic potential for scalar particles in a crossed electromagnetic field, including non-perturbative corrections and boundary condition effects.

Contribution

It presents a novel high-temperature expansion incorporating non-perturbative effects for scalar particles in crossed fields, considering boundary conditions and particle-antiparticle contributions.

Findings

Non-perturbative corrections depend on boundary conditions.

Vacuum energy and thermodynamic potential are expanded at high temperatures.

Particle and antiparticle contributions are analyzed separately.

Abstract

The problem of a scalar particle in a constant crossed electromagnetic field ($\mathbf{E}\perp\mathbf{H}$ and $|\mathbf{E}|=|\mathbf{H}|$) is examined. The high-temperature expansion of the grand thermodynamic potential and vacuum energy with account for non-perturbative corrections are derived. The contribution from particles and antiparticles is considered separately. It is shown that the non-perturbative corrections depend on boundary conditions but do not depend on fields.