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 $\left(K_{F}\right)_{\mu\nu\alpha\beta}$. 
K. Bakke and H. Belich
hep-th quant-ph