Noncommutative Electrodynamics from $SO(2,3)_\star$ Model of Noncommutative Gravity

TL;DR

This paper extends a noncommutative gravity model to include matter fields, deriving first-order corrections that lead to a novel noncommutative electrodynamics with observable effects like modified Landau levels and magnetic moments.

Contribution

It introduces matter fields into the $SO(2,3)_\star$ noncommutative gravity model and derives first-order noncommutative corrections for fermions and gauge fields.

Findings

First non-vanishing NC corrections are linear in the noncommutativity parameter.

Derived a non-standard NC Electrodynamics in flat spacetime.

Calculated NC effects on Landau levels and electron magnetic dipole moment.

Abstract

In our previous work we have constructed a model of noncommutative (NC) gravity based on $SO(2,3)_\star$ gauge symmetry. In this paper we extend the model by adding matter fields: fermions and a $U(1)$ gauge field. Using the enveloping algebra approach and the Seiberg-Witten map we construct actions for these matter fields and expand the actions up to first order in the noncommutativity (deformation) parameter. Unlike in the case of pure NC gravity, first non-vanishing NC corrections are linear in the noncommutativity parameter. In the flat space-time limit we obtain a non-standard NC Electrodynamics. Finally, we discuss effects of noncommutativity on relativistic Landau levels of an electron in a constant background magnetic field and in addition we calculate the induced NC magnetic dipole moment of the electron.