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 µ 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 µ , we are able to perform calculations perturbatively in v µ up to second order. We also find results without recourse to approximations for two special cases, that of the mirror and v µ 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.PACS numbers:
I. INTRODUCTIONLorentz symmetry violating (LV) field theories have been recently received substantial attention as a possible signature for underlying physics arising from the Planck scale. The search for Lorentz violation effects have been developed in several branches of physics mainly in the framework of the Standard Model Extension (SME) [1-4]: we mention, for instance, QED effects [5-7, 9, 10], radiative corrections [11][12][13], the study of Lorentz symmetry violation with boundary conditions [14], and effects in classical electrodynamics [15][16][17][18], among many others. In particular, scalar fields are particularly interesting for exploring the fundamental theoretical properties of field theories with Lorentz invariance [19][20][21][22][23][24][25][26][27][28][29][30] and, for the case of the Higgs fields, also for phenomenology [31,32].Regarding scalar field theories in a Lorentz symmetry breaking scenario, some recent works [33, 34] considered a model composed by a massive real scalar field Lagrangian augmented by the aether-like CPT-even Lorentz symmetry breaking term, which is a coupling between the derivative of the scalar field and a constant background vector v µ , and studying the Casimir effect both for zero [33] and finite temperature [34]. Inspired by these works, also using a scalar field as the theoretical setup, one of the most fundamental questions one can ask concerns the physical phenomena produced by the presence of point-like sources, mainly the possible emergence of phenomena with no counterpart in the standard, Lorentz invarian...
