Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension

We discuss the appearance of relativistic geometric quantum phases for a Dirac neutral particle based on possible scenarios of the Lorentz symmetry violation background in the CPT-even gauge sector of Standard Model Extension. Relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the the parity-even and parity-odd sectors of the tensor ${\left(K_F\right)}_{\mu \nu \alpha \beta }$.