Semi-Classical Dirac Vacuum Polarisation in a Scalar Field

Lampart, Jonas; Lewin, Mathieu

doi:10.1007/s00023-016-0472-y

Cited by 1 publication

(1 citation statement)

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“…This regime of strong magnetic fields has been the object of several recent studies in different situations [48,26,64,70,16,17,18,19,24,23,25,39], none of them covering the continuous spectrum of the Dirac operator, to our knowledge. A result similar to (7) has recently been obtained in the simpler case of a scalar field in [45], which is a more conventional semiclassical limit.…”

Section:     supporting

confidence: 66%

Derivation of the magnetic Euler–Heisenberg energy

Gravejat

Lewin

Séré

2018

Journal de Mathématiques Pures et Appliquées

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In quantum field theory, the vacuum is a fluctuating medium which behaves as a nonlinear polarizable material. In this article, we perform the first rigorous derivation of the magnetic Euler-Heisenberg effective energy, a nonlinear functional that describes the effective fluctuations of the quantum vacuum in a classical magnetic field.We start from a classical magnetic field in interaction with a quantized Dirac field in its ground state, and we study a limit in which the classical magnetic field is slowly varying. After a change of scales, this is equivalent to a semi-classical limit → 0, with a strong magnetic field of order 1/ . In this regime, we prove that the energy of Dirac's polarized vacuum converges to the Euler-Heisenberg functional. The model has ultraviolet divergences, which we regularize using the Pauli-Villars method. We also discuss how to remove the regularization of the Euler-Heisenberg effective Lagrangian, using charge renormalization, perturbatively to any order of the coupling constant.

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