Hamiltonian analysis of the BFCG formulation of General Relativity
arXiv:1807.06354 · doi:10.1088/1361-6382/aaee25
Abstract
We perform the complete Hamiltonian analysis of the BFCG action for General Relativity. We determine all the constraints of the theory and classify them into the first-class and the second-class constraints. We also show how the canonical formulation of BFCG General Relativity reduces to the Einstein-Cartan and triad canonical formulations. The reduced phase space analysis also gives a 2-connection which is suitable for the construction of a spin-foam basis which will be a categorical generalization of the spin-network basis from Loop Quantum Gravity.
arXiv commentv2: published version, 21 pages
References in corpus (16)
- Loop Quantum Cosmology: A Status Report
- Real Ashtekar Variables for Lorentzian Signature Space-times
- The Spin Foam Approach to Quantum Gravity
- An Invitation to Higher Gauge Theory
- so(4) Plebanski Action and Relativistic Spin Foam Model
- Testing loop quantum cosmology
- A holographic formulation of quantum general relativity
- Topological Higher Gauge Theory - from BF to BFCG theory
- Barrett-Crane spin foam model from generalized BF-type action for gravity
- Poincare 2-group and quantum gravity
- Holographic Formulation of Quantum Supergravity
- Hybrid Models in Loop Quantum Cosmology
- Effective action and semiclassical limit of spin foam models
- Spin-cube Models of Quantum Gravity
- Canonical formulation of Poincare BFCG theory and its quantization
- Hamiltonian analysis of the BFCG theory for the Poincare 2-group
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- Higher form Yang-Mills as higher BFYM theories
- Gauge symmetry of the 3BF theory for a generic Lie 3-group
- 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
- Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity