# Aharonov-Bohm scattering for relativistic particles in (3 + 1)-dimensional noncommutative space with spin dependence

## TL;DR

This paper investigates how noncommutative spacetime with spin effects influences Aharonov-Bohm scattering of relativistic particles, revealing Lorentz-preserving models with unique noncommutativity parameters.

## Contribution

It introduces a Lorentz-symmetric noncommutative model incorporating spin in (3+1) dimensions and computes the scattering amplitude for small magnetic flux.

## Key findings

- Noncommutativity affects scattering amplitudes.
- Model preserves Lorentz symmetry despite nonconstant noncommutativity.
- Comparison with canonical noncommutativity highlights differences.

## Abstract

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