# Gauge symmetry of the 3BF theory for a generic semistrict Lie three-group

@article{Radenkovi2022GaugeSO, title={Gauge symmetry of the 3BF theory for a generic semistrict Lie three-group}, author={Tijana Radenkovi{\'c} and Marko Vojinovi{\'c}}, journal={Classical and Quantum Gravity}, year={2022}, volume={39} }

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 three-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 three-group is performed, by using the Dirac procedure. The Hamiltonian analysis is the first step towards a canonical quantization of a 3BF theory…

## One Citation

### Topological invariant of 4-manifolds based on a 3-group

- MathematicsJournal of High Energy Physics
- 2022

Abstract
We study a generalization of 4-dimensional BF-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum Z, based on the classical 3BF…

## References

SHOWING 1-10 OF 52 REFERENCES

### Hamiltonian Analysis for the Scalar Electrodynamics as 3BF Theory

- PhysicsSymmetry
- 2020

The complete Hamiltonian analysis of the 3BF action for the choice of a Lie 3-group corresponding to scalar electrodynamics is performed and it is shown that the resulting dynamic constraints eliminate all propagating degrees of freedom.

### Higher gauge theories based on 3-groups

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe study the categorical generalizations of a BF theory to 2BF and 3BF theories, corresponding to 2-groups and 3-groups, in the framework of higher gauge theory. In particular, we construct…

### An invitation to higher gauge theory

- Mathematics
- 2011

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge…

### Standard Model and 4-groups

- Mathematics, Physics
- 2020

We show that a categorical generalization of the the Poincaré symmetry which is based on the n-crossed modules becomes natural and simple when n = 3 and that the corresponding 3-form and 4-form gauge…

### Hamiltonian analysis of the BFCG theory for the Poincaré 2-group

- Physics
- 2015

We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincaré 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The…

### Lie crossed modules and gauge-invariant actions for 2-BF theories

- Mathematics
- 2010

We generalize the BF theory action to the case of a general Lie crossed module $(H \to G)$, where $G$ and $H$ are non-abelian Lie groups. Our construction requires the existence of $G$-invariant…

### Poincaré 2-group and quantum gravity

- Physics
- 2011

We show that general relativity can be formulated as a constrained topological theory for flat 2-connections associated with the Poincaré 2-group. Matter can be consistently coupled to gravity in…

### Hamiltonian analysis of the BFCG formulation of general relativity

- PhysicsClassical and Quantum Gravity
- 2018

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…

### Canonical formulation of Poincaré BFCG theory and its quantization

- Physics
- 2014

We find the canonical formulation of the Poincaré BFCG theory in terms of the spatial 2-connection and its canonically conjugate momenta. We show that the Poincaré BFCG action is dynamically…

### Modern Canonical Quantum General Relativity

- Physics
- 2008

The open problem of constructing a consistent and experimentally tested quantum theory of the gravitational field has its place at the heart of fundamental physics. The main approaches can be roughly…