Deformed Maxwell Algebras and their Realizations

Understand

We study all possible deformations of the Maxwell algebra.

• In D=d+1\neq 3 dimensions there is only one-parameter deformation.
• The deformed algebra is isomorphic to so(d+1,1)\oplus so(d,1) or to so(d,2)\oplus so(d,1) depending on the signs of the deformation parameter.
• We construct in the dS (AdS) space a model of massive particle interacting with Abelian vector field via non-local Lorentz force.