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's 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 realises the
violation of Lorentz symmetry.Comment: 8 pages, added references, no figure