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

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

2010-03-11

arxiv.org/abs/1003.2412v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

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. We show that the structure of the constraints of a SO(4,1) constrained BF theory is exactly that of gravity in Holst formulation. We also briefly discuss quantization of the theory.

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