New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario
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PARTICLES AND FIELDS
New Effects in the Vicinity of a Perfectly Conducting Plate in a Non-minimal Lorentz Violation Scenario L. H. C. Borges1
· F. A. Barone2
Received: 9 March 2020 / Published online: 5 August 2020 © Sociedade Brasileira de F´ısica 2020
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. Keywords Electromagnetic field · Non-minimal Lorentz violation · Conducting plate · Functional generator · Boundary conditions · Interaction energy · Image method
1 Introduction The Lorentz symmetry breaking has been an issue of permanent interest in the latest years in many contexts. In this scenario, we can obtain a wide range of physical phenomena from the so-called Standard Model Extension (SME) [2, 3]. We can mention, for instance, effects related to the classical electrodynamics [4–8], the propagation of field waves [9–16], signs of Lorentz symmetry breaking in atomic and molecular physics [17–21], modifications in
L. H. C. Borges
[email protected] F. A. Barone [email protected] 1
Centro de Ciˆencias Naturais e Humanas, Universidade Federal do ABC, Rua Santa Ad´elia, 166, Santo Andr´e, SP, 09210-170, Brazil
2
IFQ - Universidade Federal de Itajub´a, Av. BPS 1303, Pinheirinho, Caixa Postal 50, Itajub´a, MG, 37500-903, Brazil
the Casimir effect [22–30], dimensional reduction [31, 32], scattering process [33–36], among others. The SME, understood as an effective field theory, includes renormalizable interactions as well as terms with higher order derivatives and non renormalizable, called non-minimal terms. By dimensional analysis, we could expect that the non-minimal terms would be subdominant in comparison with the minimal ones present in the SME. So,
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