Distinguished Hamiltonian theorem for homogeneous symplectic manifolds

Abstract

A diffeomorphism of a finite-dimensional flat symplectic manifold which is canonoid with respect to all linear and quadratic Hamiltonians preserves the symplectic structure up to a factor: so runs the "quadratic Hamiltonian theorem". Here we show that the same conclusion holds for much smaller "sufficiency subsets" of quadratic Hamiltonians, and the theorem may thus be extended to homogeneous infinite-dimensional symplectic manifolds. In this way we identify the distinguished Hamiltonians for the Kähler manifold of equivalent quantizations of a Hilbertizable symplectic space.