Lorentz symmetry violations and applications in planar physics
We start by giving a general description of Lorentz symmetry violation (LV), mentioning how it can be implemented through spontaneous relativistic symmetry breaking. We first present the phenomenological approach to the VL, which consists of inserting the VL effects directly into the dispersion relations of electromagnetic waves. Then we review the more general approach to LV, the Standard Model Extension (SME). By means of the SME, we show that a modification in Maxwell's Lagrangian can lead to birefringence effects in vacuum. Motivated by applications of LV in condensed matter systems such as Weyl semimetals, we study the consequences of adding a non-minimum term of mass dimension 5 with LV in models in (2+1) dimensions. For this, we use the dimensional reduction procedure, which consists of obtaining such a model starting from a Lagrangian in (3+1) dimensions. Once the Lagrangian is obtained, we accurately calculate the propagator of the theory and use it to calculate physical quantities such as forces and torques between charged particles, using point loads and Dirac points. We show that the addition of such a term to the Lagrangian leads to corrections of forces between charges, as well as to torques that do not exist in usual electrodynamics.