# High-temperature expansion of the one-loop effective action induced by scalar and Dirac particles

## TL;DR

This paper derives comprehensive nonperturbative high-temperature expansions for the one-loop effective action induced by charged scalar and Dirac particles, accounting for boundary conditions and finite temperatures, with explicit results for vacuum energies and divergences.

## Contribution

It provides the first complete nonperturbative high-temperature expansion formulas for scalar and Dirac particles including boundary effects and vacuum energy calculations.

## Key findings

- Explicit expressions for vacuum energies of Dirac fermions are obtained.
- Boundary conditions significantly affect the high-temperature expansion corrections.
- The naive fermionic effective action diverges as fermion mass approaches zero.

## Abstract

The complete nonperturbative expressions for the high-temperature expansion of the one-loop effective action induced by the charged scalar and the charged Dirac particles both at zero and finite temperatures are derived with account for possible nontrivial boundary conditions. The background electromagnetic field is assumed to be stationary and such that the corresponding Klein-Gordon operator or the Dirac Hamiltonian are self-adjoint. The contributions of particles and antiparticles are obtained separately. The explicit expressions for the $C$-symmetric and the non $C$-symmetric vacuum energies of the Dirac fermions are derived. The leading corrections to the high-temperature expansion due to the nontrivial boundary conditions are explicitly found. The corrections to the logarithmic divergence of the effective action that come from the boundary conditions are derived. The high-temperature expansion of the naive one-loop effective action induced by charged fermions turns out to be divergent in the limit of a zero fermion mass.