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

Understand

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.