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

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.