New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario

Abstract

In this paper we consider some physical phenomena in the vicinity of a conducting plate in a non-minimal Lorentz-violating scenario in 3+1 dimensions. We consider a model where the dynamics of the abelian gauge field is given by the standard Maxwell Lagrangian added by a Lorentz symmetry breaking term with the presence of higher order derivatives in the gauge field. The Lorentz symmetry breaking is due to the presence of a single background vector d λ and we perform the calculations perturbatively up to first order in d λ. We obtain the propagator for the gauge field in the presence of a mirror and the interaction force between the mirror and a point-like electric charge, as well as the interaction force between the mirror and an electric dipole. We show that, on the contrary to what happens in a minimal Lorentz-violating scenario with one single background field (L.H.C. Borges, F.A. Barone, Eur. Phys. J. C 693, 77, 2017), the image method is not valid in the model that we consider in this paper. As a consequence, the symmetry of spatial reflection on the mirror is broken. We also investigate the emergence of a torque in a system composed by a mirror and a point-like electric charge, placed at a fixed distance apart each other. The results obtained in this work have no counterpart in the Maxwell electrodynamics and were not verified in any Lorentz-violating scenario previously.

The Lorentz-violating real scalar field at thermal equilibrium

“…For instance, by considering the case in which all diagonal terms are equal to κ 11 , and respectively all offdiagonal terms are κ 12 , we find that the suitable conditions are κ 11 −κ 12 < 1, and κ 11 +2κ 12 < 1. On the other hand, by considering arbitrary diagonal terms, κ 11 , κ 22 , κ 33 , and all the off-diagonal terms vanishing except for κ 12 = κ 21 , we find a well behaved particle spectrum if κ 33 < 1, κ 11 + κ 22 < 1 and κ 11 +κ 22 +(κ 12 ) 2 −κ 11 κ 22 < 1. Also, tachyonic modes must appear whenever the argument in square root of ( 18) is negative.…”

“…The effects of Lorentz violation has been widely investigated in several different scenarios. It is worth mentioning recent studies on the statistical mechanics in LV background [10][11][12][13][14], the Casimir effect [15][16][17][18][19][20], the Bose-Einstein condensation [21][22][23][24][25], QED sector [26][27][28][29][30], LV theories with boundary conditions [31][32][33][34], Chern-Simons-like terms [35][36][37][38][39], scattering processes [40][41][42][43][44], geometrical correspondences [45,46], supersymmetric LV models [47][48][49][50][51], as well as many others interesting subjects (see also [52] and references therein for a more exhaustive list of related papers).…”

Magnetoelectric boundary simulated by a Chern–Simons-like model

“…It is due to the magnetoelectric properties of the plate and is a θ -dependent contribution, the mean angle between the spin of the state (36) and the normal to the plate. From the third term in (37) we have a mean contribution to the force between the plate and particle which falls with the distance between them slower in comparison with the second term in (37). Besides, this force also depends on the θ angle.…”

“…In the present section we consider the interaction energy between a stationary point-like charge and the semi-transparent mirror studied in the previous section. Since we have a quadratic Lagrangian in the field variables, as discussed in references [27][28][29][30][31][32][33][34][35][36][37][38], the contribution due to the external sources to the ground state energy of the system is given by…”

“…In addition to a force, from the third term in (37), we also obtain a mean torque acting on the quantum particle with respect to the angle θ . This torque is always non-positive, attains its minimum value for θ = π/2 and vanishes when θ = 0, π.…”