Eur. Phys. J. C (2005) 42: 127-137
https://doi.org/10.1140/epjc/s2005-02253-6

Theoretical Physics

Classical solutions in a Lorentz violating scenario of Maxwell-Chern-Simons-Proca electrodynamics

¹ Departamento de Física e Química, Universidade Federal do Espírito Santo (UFES), Av. Fernando Ferrari, 29060-900, S/N Goiabeiras, Vitória - ES, Brasil
² Universidade Federal de Juiz de Fora (UFJF), Colégio Técnico Universitário, av. Bernardo Mascarenhas 1283, 36080-001, Bairro Fábrica - Juiz de Fora - MG, Brasil
³ Universidade Federal do Maranhão (UFMA), Departamento de Física, Campus Universitário do Bacanga, 65085-580, São Luiz MA, Brasil
⁴ CBPF - Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, CEP 22290-180, Rio de Janeiro, RJ, Brasil

^* e-mail: belich@cce.ufes.br

Abstract

Taking as starting point the planar model that arises from the dimensional reduction of the Abelian-Higgs Carroll-Field-Jackiw model, we write down and study the extended Maxwell equations and the associated wave equations for the potentials. The solutions for these equations correspond to the usual ones for the MCS-Proca system, supplemented with background-dependent correction terms. In the case of a purely timelike background, exact algebraic solutions are presented which possess a similar behavior to the MCS-Proca counterparts near and far from the origin. On the other hand, for a purely spacelike background, only approximate solutions are feasible. They consist of non-trivial analytic expressions with manifest evidence of spatial anisotropy, which is consistent with the existence of a privileged direction in space. These solutions also behave similarly to the MCS-Proca ones near and far from the origin.