Exotic Galilean Conformal Symmetry and its Dynamical Realisations

TL;DR

This paper explores an extended Galilean conformal algebra in (2+1) dimensions, providing models with higher derivatives, Coulomb and magnetic interactions, and analyzing effects of external electromagnetic fields.

Contribution

It introduces a ten-dimensional Galilean conformal algebra extension and offers explicit dynamical realizations including interactions and external fields.

Findings

Extended algebra includes dilatation, expansion, acceleration generators, and a central charge.

Models with higher derivatives and Coulomb/magnetic vortex interactions realize the symmetry.

External electromagnetic fields modify the algebra and its realizations.

Abstract

The six-dimensional exotic Galilean algebra in (2+1) dimensions with two central charges $m$ and $\theta$, is extended when $m=0$, to a ten-dimensional Galilean conformal algebra with dilatation, expansion, two acceleration generators and the central charge $\theta$. A realisation of such a symmetry is provided by a model with higher derivatives recently discussed in \cite{peterwojtek}. We consider also a realisation of the Galilean conformal symmetry for the motion with a Coulomb potential and a magnetic vortex interaction. Finally, we study the restriction, as well as the modification, of the Galilean conformal algebra obtained after the introduction of the minimally coupled constant electric and magnetic fields.