Magnetic properties of confined bosonic vacuum at finite temperature

TL;DR

This paper investigates how confinement, magnetic fields, and temperature influence the vacuum properties of a charged scalar field, deriving corrections to the effective Lagrangian and revealing temperature effects on vacuum permeability.

Contribution

It introduces a comprehensive calculation of the vacuum's magnetic properties considering confinement, magnetic field, and temperature, extending the Heisenberg-Euler framework with finite temperature corrections.

Findings

Finite temperature affects vacuum permeability.

Confinement introduces significant corrections to the effective Lagrangian.

Results generalize the Heisenberg-Euler effective action to finite temperature and confinement.

Abstract

We compute the combined effect of confinement, an external magnetic field and temperature on the vacuum of the charged scalar field using Schwinger's formula for the effective action in the imaginary time formalism. The final result reproduces an effective Lagrangian similar to the Heisenberg-Euler one in the limit of no confinement, in the case of confinement it provides the necessary corrections to this Lagrangian at each order of magnitude of the magnetic field. The results show a finite temperature contribution to the vacum permeability constant apart from the one due to confinement alone.