Eur. Phys. J. C (2005) 41: 421-426
https://doi.org/10.1140/epjc/s2005-02240-y

theoretical physics

Non-minimal coupling to a Lorentz-violating background and topological implications

¹ Departamento de Física e Química, Universidade Federal do Espírito Santo (UFES), Av. Fernando Ferrari, 29060-900, Vitória - ES, S/N Goiabeiras, Brasil
² Grupo de Física Teórica José Leite Lopes, C.P.91933, CEP 25685-970, Petrópolis, RJ, Brasil
³ CCP, CBPF, Rua Xavier Sigaud 150, CEP 22290-180, Rio de Janeiro, RJ, Brasil
⁴ Colégio Técnico Universitário, Universidade Federal de Juiz de Fora (UFJF), av. Bernardo Mascarenhas 1283, 36080-001, Bairro Fábrica - Juiz de Fora - MG, [INAME]Universidade Federal de Juiz de Fora (UFJF)[/INAME] [IDIVISION]Colégio Técnico Universitário[/IDIVISION] [ISTREET]av. Bernardo Mascarenhas 1283[/ISTREET] [ICITY]Bairro Fábrica - Juiz de Fora - MG[/ICITY] [IPOSTCODE]36080-001[/IPOSTCODE] [ICOUNTRY]Brasil[/ICOUNTRY] [ISTATE], Brasil
⁵ Departamento de Fí sica, Universidade Federal do Maranhão (UFMA), Campus Universitário do Bacanga, 65085-580, São Luiz - MA, Brasil

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

Abstract

The non-minimal coupling of fermions to a background responsible for the breaking of Lorentz symmetry is introduced in Dirac’s equation; the non-relativistic regime is contemplated, and the Pauli equation is used to show how an Aharonov-Casher phase may appear as a natural consequence of the Lorentz violation, once the particle is placed in a region where there is an electric field. Different ways of implementing the Lorentz breaking are presented and, in each case, we show how to relate the Aharonov-Casher phase to the particular components of the background vector or tensor that realizes the violation of Lorentz symmetry.