  We study a gravitational action which is a linear combination of the
Hilbert-Palatini term and a term quadratic in torsion and possessing local
Poincare invariance. Although this action yields the same equations of motion
as General Relativity, the detailed Hamiltonian analysis without gauge fixing
reveals some new points never shown in the Hilbert-Palatini formalism. These
include that an additional term containing torsion appears in the spatial
diffeomorphism constraint and that the primary second-class constraints have to
be imposed in a manner different from that in the Hilbert-Palatini case. These
results may provide valuable lessons for further study of Hamiltonian systems
with torsion.
