Anandan quantum phase and quantum holonomies induced by the effects of the Lorentz symmetry violation background in the CPT-even gauge sector of the Standard Model Extension

We study the rise of geometric quantum phases corresponding to the analogues of the Anandan quantum phase (J. Anandan, Phys. Lett. A 138, 347 (1989)) based on possible scenarios of the Lorentz symmetry violation background in the CPT-even gauge sector of the Standard Model Extension. We also show that we can obtain quantum holonomies associated with the analogues of the Anandan quantum phase, and discuss a possible analogy with the holonomic quantum computation (P. Zanardi, M. Rasetti, Phys. Lett. A 264, 94 (1999))