Gauge fields and infinite chains of dualities

TL;DR

This paper demonstrates that Maxwell's theory particle states can be represented through infinitely many gauge fields and duality relations, extending to higher dimensions and form fields, with implications for particle representations.

Contribution

It introduces a novel formulation of particle states using infinite gauge fields and dualities, including a pedagogical approach to Lorentz and gauge covariant representations.

Findings

Infinite gauge field representations for Maxwell's theory.

Duality relations formulated as first order in derivatives.

Extension to eleven-dimensional three-form fields.

Abstract

We show that the particle states of Maxwell's theory, in $D$ dimensions, can be represented in an infinite number of ways by using different gauge fields. Using this result we formulate the dynamics in terms of an infinite set of duality relations which are first order in space-time derivatives. We derive a similar result for the three form in eleven dimensions where such a possibility was first observed in the context of E11. We also give an action formulation for some of the gauge fields. In this paper we give a pedagogical account of the Lorentz and gauge covariant formulation of the irreducible representations of the Poincar\'e group, used previously in higher spin theories, as this plays a key role in our constructions. It is clear that our results can be generalised to any particle.