Constraint analysis of two-dimensional quadratic gravity from $${ BF}$$ B F theory

Abstract

Quadratic gravity in two dimensions can be formulated as a Background Field (BF ) theory plus an interaction term which is polynomial in both, the gauge and Background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell-Mansouri gravity in four dimensions.In this article we use the Dirac's Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin-Fradkin-Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.

Hamilton-Jacobi analysis of the four-dimensional BF model with cosmological term

“…Usually, this procedure is made with 1 gb9950@gmail.com 2 pimentel@ift.unesp.br 3 valcarcel.flores@gmail.com the Hamiltonian Dirac formalism [9] (also see [10]). The Hamiltonian analysis of Plebanski theory has been made in [11], the Freidel-Starodubtsev in [12], the two-dimensions Polynomial BF in [13] and the BF with cosmological term in [14]. However, there are other methods of constraint analysis, as the Hamilton-Jacobi formalism.…”