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

In this paper we consider classical effects in a model for a scalar field incorporating Lorentz symmetry breaking due to the presence of a single background vector vμ coupled to its derivative. We investigate 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 a 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 vμ, we are able to perform calculations perturbatively in vμ up to second order, and we also present exact results specific cases. 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.