Abstract
We study all possible deformations of the Maxwell algebra. In D = d+1≠3 dimensions there is only one-parameter deformation. The deformed algebra is isomorphic to so(d+1,1)⊕so(d,1) or to so(d,2)⊕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. In D = 2+1 the deformations depend on two parameters b and k. We construct a phase diagram, with two parts of the (b,k) plane with so(3,1)⊕so(2,1) and so(2,2)⊕so(2,1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2,1)⊕so(2,1). We introduce in D = 2+1 the Volkov-Akulov type model for a Abelian Goldstone-Nambu vector field described by a non-linear action containing as its bilinear term the free Chern-Simons Lagrangean.
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