Dynamical structure of Carrollian Electrodynamics

TL;DR

This paper develops an action for ultra-relativistic electrodynamics on Carroll manifolds, revealing Hamiltonian conformal symmetry and an infinite set of conserved charges in four dimensions.

Contribution

It introduces a new Carrollian electrodynamics model with a Hamiltonian conformal algebra and conserved charges, expanding understanding of ultra-relativistic limits.

Findings

The model has two physical degrees of freedom per space point.

The conformal Carroll algebra acts Hamiltonianly on phase space in 4D.

The algebra generates an infinite number of conserved charges.

Abstract

We present an action of ultra-relativistic electrodynamics on a flat Carroll manifold. The model exhibits a couple of physical degrees of freedom per space-point. We observe that the action of the conformal Carroll algebra on the phase space is Hamiltonian in 4 space-time dimensions. Moreover the elements of the algebra give rise to an infinite number of conserved charges and the charge algebra is an exact realization of the kinematical algebra.