Hamiltonian Analysis for the Scalar Electrodynamics as 3<i>BF</i> Theory

Abstract

The higher category theory can be employed to generalize the B F action to the so-called 3 B F 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 3 B F theory for a specific choice of the gauge 3-group. The complete Hamiltonian analysis of the 3 B F 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 3 B F theory, an important stepping stone for the quantization of the complete scalar electrodynamics coupled to Einstein–Cartan gravity formulated as a 3 B F action with suitable simplicity constraints. It is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom, i.e., the 3 B F theory for this choice of a 3-group is a topological field theory, as expected.

Keywords

• Hamiltonian analysis
• higher gauge theory
• BF theory
• topological theory
• scalar electrodynamics