Canonical formulation of Poincare BFCG theory and its quantization
arXiv:1409.3751 · doi:10.1007/s10714-015-1900-x
Abstract
We find the canonical formulation of the Poincare BFCG theory in terms of the spatial 2-connection and its canonically conjugate momenta. We show that the Poincare BFCG action is dynamically equivalent to the BF action for the Poincare group and we find the canonical transformation relating the two. We study the canonical quantization of the Poincare BFCG theory by passing to the Poincare-connection basis. The quantization in the 2-connection basis can be then achieved by performing a Fourier transform. We also briefly discuss how to approach the problem of constructing a basis of spin-foam states, which are the categorical generalization of the spin-network states from Loop Quantum Gravity.
arXiv comment17 pages, errors corrected and new references added
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Cited by in corpus (11)
- Higher Gauge Theories Based on 3-groups
- Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
- Hamiltonian analysis of the BFCG theory for the Poincare 2-group
- Hamiltonian analysis of the BFCG formulation of General Relativity
- Topological invariant of 4-manifolds based on a 3-group
- Standard Model and 4-groups
- Higher form Yang-Mills as higher BFYM theories
- Gauge symmetry of the 3BF theory for a generic Lie 3-group
- Higher Chern-Simons based on (2-)crossed modules
- Symmetry breaking mechanisms of the 3BF action for the Standard Model coupled to gravity
- Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity