Boundary-free Parts Research Articles

Casimir densities for a conducting plate in de Sitter spacetime

Two-point functions for the electromagnetic field in background of (D + 1)-dimensional dS spacetime are evaluated assuming that the field is prepared in the Bunch-Davies vacuum state. By using these functions, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor are investigated in the geometry of a conducting plate. The VEVs are explicitly decomposed into the boundary-free and plate-induced parts. For points outside of the plate the renormalization is needed for the first parts only. Because of the maximal symmetry of the background spacetime and of the Bunch-Davies vacuum state, the boundary-free parts do not depend on spacetime coordinates, whereas the plate-induced parts are functions of the proper distance of the observation point from the plate. The plate-induced part in the VEV of the energy-momentum tensor vanishes for D = 3 which is a direct consequence of a conformal invariance of the electromagnetic field for this spatial dimension. For D > 3, in addition to the diagonal components, the vacuum energy-momentum tensor has nonzero off-diagonal component which describes energy flux along the direction normal to the plate.

Fermionic Casimir densities in a conical space with a circular boundary and magnetic flux

The vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field is investigated in a ($2+1$)-dimensional conical spacetime in the presence of a circular boundary and an infinitely thin magnetic flux located at the cone apex. The MIT bag boundary condition is assumed on the circle. At the cone apex we consider a special case of boundary conditions for irregular modes, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The presence of the magnetic flux leads to the Aharonov-Bohm-like effect on the VEV of the energy-momentum tensor. For both exterior and interior regions, the VEV is decomposed into boundary-free and boundary-induced parts. Both these parts are even periodic functions of the magnetic flux with the period equal to the flux quantum. The boundary-free part in the radial stress is equal to the energy density. Near the circle, the boundary-induced part in the VEV dominates and for a massless field the vacuum energy density is negative inside the circle and positive in the exterior region. Various special cases are considered.

FERMIONIC CONDENSATE AND INDUCED CURRENT IN A CONICAL SPACE WITH A CIRCULAR BOUNDARY AND MAGNETIC FLUX

The fermionic condensate and current density are investigated in a (2 + 1)-dimensional conical spacetime in the presence of a circular boundary and a magnetic flux. On the boundary the fermionic field obeys the MIT bag boundary condition. For irregular modes, we consider a special case of boundary conditions at the cone apex, when the MIT bag boundary condition is imposed at a finite radius, which is then taken to zero. The condensate and current are periodic functions of the magnetic flux with the period equal to the flux quantum. For both exterior and interior regions, the expectation values are decomposed into boundary-free and boundary-induced parts. In the case of a massless field the boundary-free part in the vacuum expectation value of the charge density vanishes, whereas the presence of the boundary induces nonzero charge density. At distances from the boundary larger than the Compton wavelength of the fermion particle, the condensate and current decay exponentially, with the decay rate depending on the opening angle of the cone.