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

Abstract

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.

9 pages

References in corpus (4)

• Topological Interpretation of Barbero-Immirzi Parameter
• 4d Lorentzian Holst action with topological terms
• From the Einstein-Cartan to the Ashtekar-Barbero canonical constraints, passing through the Nieh-Yan functional
• A New Perspective on Covariant Canonical Gravity

Cited by in corpus (9)

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• Pre-geometric Einstein-Cartan Field Equations and Emergent Cosmology
• Perturbative BF theory
• Constraint Analysis of Two-Dimensional Quadratic Gravity from BF Theory
• Non-Abelian gauge theories invariant under diffeomorphisms