Magnetic Permeability of Confined Fermionic Vacuum

We obtain using Schwinger’s proper time approach the Casimir-Euler-Heisenberg effective action of fermion fluctuations for the case of an applied magnetic field between confining plates. Aside of higher order non-linear field effects we identify a novel contribution to the vacuum permeability. These contributions are exceedingly small for normal electromagnetism due to the smallness of the electron Compton wavelength compared to the size of laboratory cavities, but their presence is thought provoking, also considering the context of strong interactions. There is a major ongoing effort [1, 2, 3] to measure the Euler-Heisenberg (EH) effect [4, 5]. As it is well understood, the EH-effective Lagrangian arises from deformation of fermion-antifermion pair fluctuations caused by an applied strong (classical = absence of virtual photon diagrams) electromagnetic field. Since renormalization defines the electric charge in an Abelian theory in the long wavelength limit, the field dependent terms in the effective action after renormalization must be of higher order than quadratic and thus introduce non-linear effects in the electromagnetic field. A (coherent) light wave within a field-filled volume experiences matter-like scattering effects from the field-polarized vacuum[6]. The hope and expectation is that the birefringence effect [7] can be experimentally observed in near future. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]