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

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.

💡 Research Summary

The paper investigates a previously under‑explored aspect of electromagnetic duality: its role as a generator of dynamics when the theory is expressed in a reduced phase‑space formulation. In the conventional Hamiltonian description of Maxwell theory the basic Poisson bracket is defined by
\