Mirrors and field sources in a Lorentz-violating scalar field theory

TL;DR

This paper explores classical effects in a Lorentz-violating scalar field theory, analyzing interactions between sources, the emergence of torques, and the validity of the image method under various configurations.

Contribution

It introduces a detailed analysis of Lorentz symmetry breaking effects on scalar fields, including interaction energies, torques, and boundary conditions, with new insights into mirror interactions.

Findings

Nontrivial torque on scalar dipoles due to Lorentz violation

Validation of the image method for Dirichlet boundary conditions in this model

Emergence of mirror-dependent torque as a novel Lorentz-violating effect

Abstract

In this paper we consider different classical effects in a model for a scalar field incorporating Lorentz symmetry breaking due to the presence of a single background vector v^{\mu} coupled to its derivative. We perform an investigation of the interaction energy between stationary steady sources concentrated along parallel branes with an arbitrary number of dimensions, and derive from this study some physical consequences. For the case of the scalar dipole we show the emergence of a nontrivial torque, which is distinctive sign of the Lorentz violation. We also investigate a similar model in the presence of a semi-transparent mirror. For a general relative orientation between the mirror and the v^{\mu}, we are able to perform calculations perturbatively in v^{\mu} up to second order. We also find results without recourse to approximations for two special cases, that of the mirror and v^{\mu} being parallel or perpendicular to each other. For all these configurations, the propagator for the scalar field and the interaction force between the mirror and a point-like field source are computed. It is shown that the image method is valid in our model for the Dirichlet's boundary condition, and we argue that this is a non-trivial result. We also show the emergence of a torque on the mirror depending on its orientation with respect to the Lorentz violating background. This is a new effect with no counterpart in theories with Lorentz symmetry in the presence of mirrors.