Generalization of the Hilbert-Palatini Action in Four-Dimensional Gravity

The generalized two-parametric Hilbert-Palatini action is
constructed, which not only includes the well-known Hilbert-Palatini and Ashtekar gravitational theory as special cases, but also gives new results. In Hamiltonian formulation, the phase space variables and the corresponding Hamiltonian constraints can be obtained, including the Ashtekar and Barbero type constraints. Moreover, the results of this action are the same as those given by the parametric canonical transformations, although these two methods are completely different.