Gauge symmetry of the 3BF theory for a generic Lie 3-group
arXiv:2101.04049 · doi:10.1088/1361-6382/ac6b78
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. In this work we determine the full gauge symmetry of the 3BF action. To that end, the complete Hamiltonian analysis of the 3BF action for an arbitrary semistrict Lie 3-group is performed, by using the Dirac procedure. This analysis is the first step towards a canonical quantization of a 3BF theory. This is an important stepping-stone for the quantization of the complete Standard Model of elementary particles coupled to Einstein-Cartan gravity, formulated as a 3BF action with suitable simplicity constraints. We show that the resulting gauge symmetry group consists of the already familiar G-, H-, and L-gauge transformations, as well as additional M- and N-gauge transformations, which have not been discussed in the existing literature.
v4: new references added, minor corrections made; 22+14 pages, 2 figures
References in corpus (11)
- LQG vertex with finite Immirzi parameter
- A New Spin Foam Model for 4d Gravity
- Higher Gauge Theory: 2-Connections on 2-Bundles
- Zakopane lectures on loop gravity
- gravity
- Topological Higher Gauge Theory - from BF to BFCG theory
- Solution to the Cosmological Constant Problem in a Regge Quantum Gravity Model
- Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory
- Canonical formulation of Poincare BFCG theory and its quantization
- Topological invariant of 4-manifolds based on a 3-group
- Standard Model and 4-groups
Cited by in corpus (6)
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- Correspondence between 3BF and Einstein-Cartan formulations of quantum gravity
- The 3BF theory as a TQFT