Hamiltonian analysis of SO(4,1) constrained BF theory

Understand

In this paper we discuss canonical analysis of SO(4,1) constrained BF theory.

• The action of this theory contains topological terms appended by a term that breaks the gauge symmetry down to the Lorentz subgroup SO(3,1).
• The equations of motion of this theory turn out to be the vacuum Einstein equations.
• By solving the B field equations one finds that the action of this theory contains not only the standard Einstein-Cartan term, but also the Holst term proportional to the inverse of the Immirzi parameter, as well as a combination of topological invariants.