  The higher category theory can be employed to generalize the BF action to the
so-called 3BF action, by passing from the notion of a gauge group to the notion
of a gauge 3-group. The theory of scalar electrodynamics coupled to
Einstein-Cartan gravity can be formulated as a constrained 3BF theory for a
specific choice of the gauge 3-group. The complete Hamiltonian analysis of the
3BF action for the choice of a Lie 3-group corresponding to scalar
electrodynamics is performed. This analysis is the first step towards a
canonical quantization of a 3BF theory, an important stepping stone for the
quantization of the complete scalar electrodynamics coupled to Einstein-Cartan
gravity formulated as a 3BF action with suitable simplicity constraints. It is
shown that the resulting dynamic constraints eliminate all propagating degrees
of freedom, i.e., the 3BF theory for this choice of a 3-group is a topological
field theory, as expected.
