Deformed Maxwell Algebras and their Realizations

TL;DR

This paper classifies all deformations of the Maxwell algebra across different dimensions, constructs models of particles interacting with vector fields in curved spaces, and introduces a nonlinear Goldstone-Nambu vector field model.

Contribution

It provides a comprehensive analysis of Maxwell algebra deformations and develops new particle interaction models in curved spacetimes, including a nonlinear vector field theory.

Findings

Unique one-parameter deformation in D=d+1≠3 dimensions.

Explicit models of particles in de Sitter and Anti-de Sitter spaces.

Phase diagram for deformations in D=2+1 with distinct algebraic structures.

Abstract

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. 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)\oplus so(2,1) and so(2,2)\oplus so(2,1) algebras separated by a critical curve along which the algebra is isomorphic to Iso(2,1)\oplus 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.