Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

Abstract

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.

arXiv commentpublished version, 21 pages

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Cited by in corpus (9)

• Topological invariant of 4-manifolds based on a 3-group
• Gauge symmetry of the 3BF theory for a generic Lie 3-group
• 3-form Yang-Mills based on 2-crossed modules
• Higher form Yang-Mills as higher BFYM theories
• Henneaux-Teitelboim gauge symmetry and its applications to higher gauge theories
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• The 3BF theory as a TQFT
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
• Construction and examples of higher gauge theories