Aharonov–Bohm Scattering for Relativistic Particles in $$(3 + 1)$$-Dimensional Noncommutative Space with Spin Dependence

Abstract

We study the effects of the noncommutativity of the spacetime with a mixed spatial and spin degrees of freedom in a relativistic situation. Using the Dirac equation in $$(3+1)$$ -D and in a symmetric gauge, we calculate the invariant amplitude for a small flux of the magnetic field. The parameter $$\theta$$ which characterizes the noncommutativity here is not constant and the model preserves Lorentz symmetry. A correlation with the scattering in the context of canonical noncommutativity is done.