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Fermionic Casimir effect in a field theory model with Lorentz symmetry violation

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 Added by A. Yu. Petrov
 Publication date 2018
  fields Physics
and research's language is English




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In this paper, we evaluate the Casimir energy and pressure for a massive fermionic field confined in the region between two parallel plates. In order to implement this confinement we impose the standard MIT bag boundary on the plates for the fermionic field. In this paper we consider a quantum field theory model with a CPT even, aether-like Lorentz symmetry violation. It turns out that the fermionic Casimir energy and pressure depend on the direction of the constant vector that implements the Lorentz symmetry breaking.



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In this paper, we investigate the thermal effect on the Casimir energy associated with a massive scalar quantum field confined between two large parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field theory. In order to do that we consider a nonzero chemical potential for the scalar field assumed to be in thermal equilibrium at some finite temperature. The calculations of the energies are developed by using the Abel-Plana summation formula, and the corresponding results are analyzed in several asymptotic regimes of the parameters of the system, like mass, separations between the plates and temperature.
We investigate combined effects of nontrivial topology, induced by a cosmic string, and boundaries on the fermionic condensate and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive fermionic field. As geometry of boundaries we consider two plates perpendicular to the string axis on which the field is constrained by the MIT bag boundary condition. By using the Abel-Plana type summation formula, the VEVs in the region between the plates are decomposed into the boundary-free and boundary-induced contributions for general case of the planar angle deficit. The boundary-induced parts in both the fermionic condensate and the energy-momentum tensor vanish on the cosmic string. Fermionic condensate is positive near the string and negative al large distances, whereas the vacuum energy density is negative everywhere. The radial stress is equal to the energy density. For a massless field, the boundary-induced contribution in the VEV of the energy-momentum tensor is different from zero in the region between the plates only and it does not depend on the coordinate along the string axis. In the region between the plates and at large distances from the string, the decay of the topological part is exponential for both massive and massless fields. This behavior is in contrast to that for the VEV of the energy-momentum tensor in the boundary-free geometry with the power law decay for a massless field. The vacuum pressure on the plates is inhomogeneous and vanishes at the location of the string. The corresponding Casimir forces are attractive.
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