Key words Geometric phase, Anandan quantum phase, Aharonov-Casher effect, permanent magnetic dipole moment, permanent electric dipole moment, Lorentz symmetry violation.We study the influence of a classical background based on the violation of the Lorentz symmetry on the relativistic Anandan quantum phase. We show that the choice of the Lorentz symmetry violation background provides an abelian contribution for the relativistic Anandan quantum phase.

In this work, we propose a CPT-even and Lorentz-violating dimension-five nonminimal coupling between fermionic and gauge fields, involving the CTP-even and Lorentz-violating gauge tensor of the SME. This nonminimal coupling modifies the Dirac equation, whose nonrelativistic regime is governed by a Hamiltonian which induces new effects, such as an electric-Zeeman-like spectrum splitting and an anomalous-like contribution to the electron magnetic moment, between others. Some of these new effects allows to constrain the magnitude of this nonminimal coupling in 1 part in 10 16 .

In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in the quantum deformed framework generated by the κ-Poincaré-Hopf algebra. We consider the nonrelativistic limit of the κ-deformed Dirac equation and use the spin-dependent term to impose an upper bound on the magnitude of the deformation parameter ε. By using the self-adjoint extension approach, we examine the scattering and bound state scenarios. After obtaining the scattering phase shift and the S-matrix, the bound states energies are obtained by analyzing the pole structure of the latter. Using a recently developed general regularization prescription [Phys. Rev. D. 85, 041701(R) (2012)], the self-adjoint extension parameter is determined in terms of the physics of the problem. For last, we analyze the problem of helicity conservation.

In this work the bound state and scattering problems for a spin-1/2 particle undergone to an Aharonov-Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin-1/2 Aharonov-Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator.The Aharonov-Bohm (AB) effect [1] (first predicted by Ehrenberg and Siday [2]) is one of most weird results of quantum phenomena. The effect reveals that the electromagnetic potentials, rather than the electric and magnetic fields, are the fundamental quantities in quantum mechanics. The interest in this issue appears in the different contexts, such as solid-state physics [3], cosmic strings [4][5][6][7][8][9][10][11][12][13][14] κ-Poincaré-Hopf algebra [15, 16], δ-like singularities [17-19], supersymmetry [20, 21], condensed matter [22, 23], Lorentz symmetry violation [24], quantum chromodynamics [25], general relativity [26], nanophysics [27], quantum ring [28-30], black hole [31, 32] and noncommutative theories [33, 34].In the AB effect of spin-1/2 particles [7], besides the interaction with the magnetic potential, an additional two dimensional δ-function appears as the mathematical description of the Zeeman interaction between the spin and the magnetic flux tube [18,19]. This interaction is the basis of the spin-orbit coupling, which causes a splitting on the energy spectrum of atoms depending on the spin state. In Ref. [17] is argued that this δ-function contribution to the potential can not be neglected when the system has spin, having shown that changes in the amplitude and scattering cross section are implied in this case. The presence of a δ-function potential singularity, turns the problem more complicated to be solved. Such kind of point interaction potential can then be addressed by the self-adjoint extension approach [35]. The self-adjoint extension of symmetric operators [36] is a very powerful mathematical method and it can be applied to various systems in relativistic and nonrelativistic quantum mechanics, supersymmetric quantum mechanics and vortex-like models.This paper extends our previous report [37] on a general physical regularization method, both in details and depth. The method has the advantage of solving problems in relativistic and nonrelativistic quantum mechanics whose Hamiltonian is s...

This Letter is based on the κ-Dirac equation, derived from the κ-Poincaré-Hopf algebra. It is shown that the κ-Dirac equation preserves parity while breaks charge conjugation and time reversal symmetries. Introducing the Dirac oscillator prescription, p → p − imωβr, in the κ-Dirac equation, one obtains the κ-Dirac oscillator. Using a decomposition in terms of spin angular functions, one achieves the deformed radial equations, with the associated deformed energy eigenvalues and eigenfunctions. The deformation parameter breaks the infinite degeneracy of the Dirac oscillator. In the case where ε = 0, one recovers the energy eigenvalues and eigenfunctions of the Dirac oscillator.