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

Abstract

We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincare 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 to those of the topological Poincare gauge theory, which is equivalent to the BFCG model at the level of the classical action, but has a very different Hamiltonian structure.

v3: Published version. 21 pages

References in corpus (4)

• Topological Higher Gauge Theory - from BF to BFCG theory
• Spin-cube Models of Quantum Gravity
• A 2-categorical state sum model
• Canonical formulation of Poincare BFCG theory and its quantization

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• Discretization of 4d Poincaré BF theory: from groups to 2-groups
• Higher Chern-Simons based on (2-)crossed modules
• Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
• On Geometry and Symmetries in Classical and Quantum Theories of Gauge Gravity
• Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity