Phase-space noncommutativity and the Dirac equation

We consider full phase-space noncommutativity in the Dirac equation, and find that in order to preserve gauge invariance, configuration space noncommutativity must be dropped. The resulting space structure gives rise to a constant magnetic field background and this effect is explicitly seen on the spectrum of the hydrogen atom. Computing this spectrum we find a bound on the momentum noncommutative parameter η  , η≲2.26 μeV/c.

► Phase-space noncommutativity.
► Dirac equation.
► Bound on the momentum noncommutative parameter, η.