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Magnetic permeability of constrained scalar QED vacuum

M. V. Cougo-Pinto·C. Farina·M. R. Negrao·A. C. Tort
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Abstract

We compute the influence of boundary conditions on the Euler-Heisenberg effective Lagrangian scalar QED scalar for the case of a pure magnetic field. The boundary conditions constrain the quantum scalar field to vanish on two parallel planes separeted by a distance $a$ and the magnetic field is assumed to be constant, uniform and perpendicular to the planes. The effective Lagrangian is obtained using Schwinger's proper-time representation and exhibits new contributions generated by the boundary condition much in the same way as a material pressed between two plates exhibits new magnetic properties. The confined bosonic vacuum presents the expected diamagnetic properties and besides the new non-linear $a$-dependent contributions to the susceptibility we show that there exists also a new $a$-dependent contribution for the vacuum permeability in the linear approximation.

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M. V. Cougo-Pinto, C. Farina, M. R. Negrao, A. C. Tort. 1999-02-03. Magnetic permeability of constrained scalar QED vacuum. https://arxiv.org/abs/hep-th/9809216

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