Hamiltonian analysis of the BFCG theory for the Poincare 2-group

TL;DR

This paper conducts a comprehensive Hamiltonian analysis of the BFCG theory for the Poincare 2-group, revealing its constraint structure and differences from the related gauge theory.

Contribution

It provides the full Hamiltonian formulation and constraint algebra of the BFCG model based on the Poincare 2-group, highlighting its unique Hamiltonian structure.

Findings

Constructed the Hamiltonian of the BFCG theory.

Computed the algebra of constraints and Dirac brackets.

Identified differences from the topological Poincare gauge theory.

Abstract

We perform the full Hamiltonian analysis of the topological BFCG action based on the Poincare 2-group. The Hamiltonian of the theory is constructed, and the algebra of constraints is computed. The Dirac brackets are evaluated, and the second class constraints are then eliminated from the theory. The results are contrasted to those of the topological Poincare gauge theory, which is equivalent to the BFCG model at the level of the classical action, but has a very different Hamiltonian structure.