Duality and integrability: Electromagnetism, linearized gravity and massless higher spin gauge fields as bi-Hamiltonian systems

TL;DR

This paper demonstrates that electromagnetism, linearized gravity, and higher spin gauge fields can be formulated as bi-Hamiltonian systems, revealing a hierarchy of integrable equations through duality symmetries in their phase space structures.

Contribution

It introduces a novel bi-Hamiltonian framework for these gauge theories, extending duality-based integrability concepts beyond electromagnetism.

Findings

Duality rotations generate Maxwell's equations in a second Poisson bracket.

Hierarchy of bi-Hamiltonian evolution equations established.

Framework extended to linearized Yang-Mills, gravity, and higher spin fields.

Abstract

In the reduced phase space of electromagnetism, the generator of duality rotations in the usual Poisson bracket is shown to generate Maxwell's equations in a second, much simpler Poisson bracket. This gives rise to a hierarchy of bi-Hamiltonian evolution equations in the standard way. The result can be extended to linearized Yang-Mills theory, linearized gravity and massless higher spin gauge fields.