Deformations of Maxwell algebra and their Dynamical Realizations

TL;DR

This paper explores all possible algebraic deformations of the Maxwell algebra across different dimensions, constructs models of particles interacting with vector fields in curved spaces, and introduces nonlinear models for Goldstone-Nambu vector fields.

Contribution

It classifies Maxwell algebra deformations in various dimensions and constructs associated dynamical models, including a nonlinear Goldstone-Nambu vector field model in 2+1 dimensions.

Findings

In D=d+1≠3, only one deformation parameter exists, leading to isomorphic algebras.

In D=2+1, deformations depend on two parameters, with a phase diagram separating different algebraic structures.

A nonlinear Volkov-Akulov type model for Goldstone-Nambu vector fields is introduced in 2+1 dimensions.

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.