Dynamical structure of Carrollian Electrodynamics

TL;DR

This work addresses the problem of realizing infinite Carrollian conformal symmetry in a dynamical field theory by constructing an action for electric-sector Carrollian electrodynamics on flat Carroll space. The authors develop a pre-symplectic (covariant phase space) framework and show that the conformal Carroll algebra acts as Hamiltonian flows on the solutions’ phase space, yielding an infinite family of conserved charges that furnish an exact realization of the kinematical Carroll algebra in four dimensions (with specific scaling dimensions). The analysis identifies precise dimensional and scaling constraints (notably Δ=(d-1)/2 for dilations and, in 3 spatial dimensions, Δ=1 for special conformal transformations) and demonstrates gauge-invariant, time-conserved charges for both the Abelian super-translations and the finite conformal generators. The results establish Carrollian electrodynamics as a concrete 4D field theory with rich infinite symmetry, with potential implications for flat-space holography and the study of BMS/Cone symmetries, and open avenues to interacting, non-Abelian, and quantum implementations.

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.