  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.
