Self-dual forms: action, Hamiltonian and compactification

It has been shown that, by adding an extra free field that decouples from the dynamics, one can construct actions for interacting 2n-form fields with self-dual field strengths in 4n+ 2 dimensions. In this paper we analyze canonical formulation of these theories, and show that the resulting Hamiltonian reduces to the sum of two Hamiltonians with independent degrees of freedom. One of them is free and has no physical consequence, while the other contains the physical degrees of freedom with the desired interactions. For the special cases of chiral scalars in two dimensions and chiral two form fields in six dimensions, we discuss compactification of these theories respectively on a circle and a two dimensional torus, and show that we recover the expected properties of these systems, including S-duality invariance in four dimensions.