Covariant hamiltonian for supergravity in d = 3 and d = 4

We extend the covariant canonical formalism recently discussed in ref. [1] to geometric theories coupled to both bosonic and fermionic p-forms. This allows a covariant hamiltonian treatment of supergravity theories. As examples we present the covariant hamiltonian formulation for d = 3 anti-De Sitter supergravity and for the “new minimal” d = 4, N = 1 supergravity (with 1-form and 2-form auxiliary fields). Form-Poisson brackets and form-Dirac brackets are defined, and used to find the form-canonical generators of all gauge symmetries via an algorithmic procedure.