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Preprints, Working Papers, ... Year : 2024

The free energy of Dirac's vacuum in purely magnetic fields

Abstract

The QED vacuum is a non-linear polarisable medium rather than an empty space. In this work, we present the first rigorous derivation of the one-loop effective magnetic Lagrangian at positive temperature, a non-linear functional describing the free energy of quantum vacuum in a classical magnetic field. We start by properly defining the free energy functional using the Pauli-Villars regularisation technique in order to remove the worst ultraviolet divergence which represents a well known issue of the theory. Then, we study the limit of slowly varying classical magnetic fields. In this regime, we prove the convergence of this functional to the Euler-Heisenberg formula with thermal corrections, by recovering the effective Lagrangian first derived by Dittrich in 1979.

Dates and versions

hal-04556630 , version 1 (23-04-2024)

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Umberto Morellini. The free energy of Dirac's vacuum in purely magnetic fields. 2024. ⟨hal-04556630⟩
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