Hamiltonian analysis of the BFCG theory for the Poincaré 2-group

We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincaré 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The Dirac brackets are evaluated, and the second class constraints are then eliminated from the theory. The results are contrasted with those of the topological Poincaré gauge theory, which is equivalent to the BFCG model at the level of the classical action, but has a very different Hamiltonian structure. (paper)