Canonical formulation of Poincare BFCG theory and its quantization

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.

17 pages, errors corrected and new references added

References in corpus (3)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• Topological Higher Gauge Theory - from BF to BFCG theory

Cited by in corpus (5)

• Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
• Topological invariant of 4-manifolds based on a 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