This paper is devoted to an investigation of the interactions between stationary sources of the electromagnetic field, in a model which exhibits explicit Lorentz-symmetry breaking due to the presence of a single background vector. We focus on physical phenomena that emerge from this kind of breaking and which have no counterpart in Maxwell electrodynamics.

We study the perturbative generation of higher-derivative Lorentz violating operators as quantum corrections to the photon effective action, originated from a specific Lorentz violation background, which has already been studied in connection with the physics of light pseudoscalars. We calculate the complete one loop effective action of the photon field through the proper-time method, using the zeta function regularization. This result can be used as a starting point to study possible effects of the Lorentz violating background we are considering in photon physics. As an example, we focus on the lowest order corrections and investigate whether they could influence the propagation of electromagnetic waves through the vacuum. We show, however, that no effects of the kind of Lorentz violation we consider can be detected in such a context, so that other aspects of photon physics have to be studied. *

Light pseudoscalars, or axion like particles (ALPs), are much studied due to their potential relevance to the fields of particle physics, astrophysics and cosmology. The most relevant coupling of ALPs from the viewpoint of current experimental searches is to the photon: in this work, we study the generation of this coupling as an effect of quantum corrections, originated from an underlying Lorentz violating background. Most interestingly, we show that the interaction so generated turns out to be Lorentz invariant, thus mimicking the standard ALPs coupling to the photon that is considered in the experiments. This consideration implies that violations of spacetime symmetries, much studied as possible consequences of physics in very high energy scales, might infiltrate in other realms of physics in unsuspected ways. Additionally, we conjecture that a similar mechanism can also generate Lorentz invariant couplings involving scalar particles and photons, playing a possible role in the phenomenology of Higgs bosons.

In this paper we consider a model which exhibits explicit Lorentz symmetry breaking due to the presence of a single background vector v μ coupled to the gauge field. We investigate such a theory in the vicinity of a perfectly conducting plate for different configurations of v μ . First we consider no restrictions on the components of the background vector and we treat it perturbatively up to second order. Next, we treat v μ exactly for two special cases: the first one is when it has only components parallel to the plate, and the second one when it has a single component perpendicular to the plate. For all these configurations, the propagator for the gauge field and the interaction force between the plate and a point-like electric charge are computed. Surprisingly, it is shown that the image method is valid in our model and we argue that it is a non-trivial result. We show there arises a torque on the mirror with respect to its positioning in the background field when it interacts with a point-like charge. It is a new effect with no counterpart in theories with Lorentz symmetry in the presence of a perfect mirror.

We investigate some aspects of the Maxwell-Chern-Simons electrodynamics focusing on physical effects produced by the presence of stationary sources and a perfectly conducting plate (mirror). Specifically, in addition to point charges, we propose two new types of point-like sources called topological source and Dirac point, and we also consider physical effects in various configurations that involve them. We show that the Dirac point is the source of the vortex field configurations. The propagator of the gauge field due to the presence of a conducting plate and the interaction forces between the plate and point-like sources are computed. It is shown that the image method is valid for the point-like charges as well as for Dirac points. For the topological source we show that the image method is not valid and the symmetry of spatial refection on the mirror is broken. In all setups considered, it is shown that the topological source leads to the emergence of torques.PACS numbers: I. INTRODUCTIONPlanar models in Quantum Field Theory have several interesting features, both theoretical and experimental. We can mention, for instance, the change in the fermions behavior in comparison with the standard classical and quantum electrodynamics [1]. One of the most important class of models of this kind is the so called Maxwell-Chern-Simons electrodynamics [2], or Abelian topological massive gauge theory [3], which is relevant because it is simultaneously massive and gauge invariant. Theoretical aspects of Maxwell-Chern-Simons electrodynamics have been investigated in Casimir effect [4][5][6][7][8][9], quantum dissipation of harmonic systems [10], quantum electrodynamics (QED 3 ) [11-15], dynamical mass generation [16,17], condensed matter physics (see, for instance, Ref.[24] and references therein), description of graphene properties [18][19][20][21][22][23], noncommutativity [25-28], strings theory [29], dynamics of vortices [30,31], and with a planar boundary [32][33][34][35][36], to mention just a few. In fact, there is a vast literature concerning this model.There is also a generalization of the Chern-Simos electrodynamics in 3 + 1 dimensions, the so called Carroll-Field-Jackiw model [37], which exhibits Lorentz symmetry breaking and whose corresponding electrostatics and magnetostatics has been studied thoroughly in reference [38], as well as the Casimir Effect, in references [39,40]. Another coupling involving the dual gauge field strength tensor in 3 + 1 dimensions is the so called axion θ-electrodynamics, which can be used to describe insulators with boundaries [41][42][43][44].In the context of Casimir Effect, in 3 + 1 dimensions, Chern-Simons surfaces can also be used to obtain Casimir repulsion setups with planar symmetry [45]. In higher dimensions, the Casimir force has been studied in Randall-Sundrum models [46], which can be interpreted as a kind of ground state for Chern-Simons gravity [47].Regarding the Maxwell-Chern-Simons electrodynamics, there are two interesting questions no yet explored in the literature, ...