Abelian geometric phase for a Dirac neutral particle in a Lorentz symmetry violation environment

We introduce a new term into the Dirac equation based on the Lorentz symmetry violation background in order to make a theoretical description of the relativistic quantum dynamics of a spin-half neutral particle, where the wave function of the neutral particle acquires a relativistic Abelian quantum phase given by the interaction between a fixed time-like 4-vector background and crossed electric and magnetic fields, which is analogous to the geometric phase obtained by Wei \textit{et al} [H. Wei, R. Han and X. Wei, Phys. Rev. Lett. \textbf{75}, 2071 (1995)] for a spinless neutral particle with an induced electric dipole moment. We also discuss the flux dependence of energy levels of bound states analogous to the Aharonov-Bohm effect for bound states.Comment: 16 pages, no figure

N=1 Supersymetric Quantum Mechanics in a Scenario with Lorentz-Symmetry Violation

We show in this paper that the dynamics of a non-relativistic particle with spin, coupled to an external electromagnetic field and to a background that breaks Lorentz symmetry, is naturally endowed with an N=1-supersymmetry. This result is achieved in a superspace approach where the particle coordinates and the spin degrees of freedom are components of the same supermultiplet.Comment: 6 pages, no figure

Lorentz symmetry breaking effects on relativistic EPR correlations

Lorentz symmetry breaking effects on relativistic EPR (Einstein-Podolsky-Rosen) correlations are discussed. From the modified Maxwell theory coupled to gravity, we establish a possible scenario of the Lorentz symmetry violation and write an effective metric for the Minkowski spacetime. Then, we obtain the Wigner rotation angle via the Fermi-Walker transport of spinors and consider the WKB ((Wentzel-Kramers-Brillouin) approximation in order to study the influence of Lorentz symmetry breaking effects on the relativistic EPR correlations.Comment: Accepted for publication in The European Physical Journal C. arXiv admin note: substantial text overlap with arXiv:1504.07432, arXiv:1504.07262, arXiv:1412.5080, arXiv:1506.0056