Casimir Effect in ModMax Electrodynamics: Background Magnetic Field Dependence

ABSTRACT We study the corrections to the vacuum energy density and the corresponding force between the plates in a Casimir apparatus in the framework of the ModMax model. We linearize the theory around a background magnetic field fixed along an arbitrary direction with respect to the z axis, taken perpendicular to the plates of the Casimir cavity. We find the mode dispersion relations of the confined electromagnetic field, from which we derive the Casimir (vacuum) energy density and the attractive force between the plates. Our results reveal that, even though the energy density and the attractive force are independent of the magnitude of the background magnetic field (due to conformal invariance), they do depend on its direction. These corrections generalize the results found in a previous study, [Phys. Rev. D 110, 116006 (2024)], where the background magnetic field was only considered either parallel or perpendicular to the axis. We compare the results with those of linear Maxwell electrodynamics for various directions of the background magnetic field. We investigate the possibility of superluminal motion of the electromagnetic field modes propagating inside the Casimir cavity in the framework of the nonlinear ModMax model.