  The formulation of gravity in 3+1 dimensions in which the spin connection is
the basic field ($\omega $-frame) leads to a theory with first and second class
constraints. Here, the Dirac brackets for the second class constraints are
evaluated and the Dirac algebra of first class constraints is found to be the
usual algebra associated to space-time reparametrizations and tangent space
rotations. This establishes the classical equivalence with the vierbein
approach (e-frame). The explicit form of the path integral for this theory is
given and the quantum equivalence with the e-frame is also established.
