New approach to the first-order canonical formulation of gravitation: Application to Einstein-Cartan-Sciama-Kibble theory

An alternative approach to the first-order canonical formulation of gravitation is developed. The vierbein e/sup mua/ and the spin connection ω/sub mua/b are treated as independent but coequal field variables. There is no partial integration of the action prior to proceeding with canonical formulation in order to rearrange the noncyclic canonical variables. The spin connection remains noncyclic, and this seems to reduce the level of calculational complexity usually encountered in the canonical formulation of gravitation theory. As a result the approach is well suited for application to extended theories, such as R+R2 theories and extended theories of supergravity. The method is applied to the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity. The Hamiltonian is obtained directly from the action following Dirac's procedure, and the consistency analysis is performed. The generators of general coordinate transformations and local Lorentz transformations, which act on both the vierbein and spin connection, arise naturally from the Lagrangian itself