Se p 19 98 Fermionic Casimir effect in an external magnetic field ∗

The influence of an external constant uniform magnetic field on the Casimir energy density of a Dirac field under antiperiodic (and periodic) boundary condition is computed by applying Schwinger’s proper time method. The result thus obtained shows that in principle, under suitable conditions, the magnetic field can enhance the fermionic Casimir energy density. Introduction The Casimir effect [1] can be generally defined as the effect of non-trivial space topology on the vacuum fluctuations of relativistic quantum fields [2, 3]. The corresponding change in the vacuum fluctuations appears as a shift in the vacuum energy density and a resulting vacuum pressure. In the case of the electromagnetic Casimir effect, there are three experiments involving metallic surfaces [4]. The results, particularly the two more recent ones, are in accord with theoretical predictions. The Casimir effect has been computed for fields other than the electromagnetic and boundary conditions different from the one implemented by conducting surfaces. The fermionic Casimir effect is of particular importance due, e.g., to the fundamental role played by the electron in QED and the quarks in QCD; it was first computed by Johnson [5] for applications in the MIT bag model [6], in which the Casimir energy density is an important ingredient. For a massless Dirac particle Johnson’s result predicts an energy density 7/4 times the energy density of the electromagnetic Casimir effect. In the case of the Casimir effect of an electrically charged quantum field it is natural and important to ask how an external electromagnetic Talk presented by A C Tort at the IV workshop on quantum field theory under the influence of external conditions e-mail: [email protected] e-mail: [email protected] e-mail: [email protected]