  We study the coupling of the gravitational action, which is a linear
combination of the Hilbert-Palatini term and the quadratic torsion term, to the
action of Dirac fermions. The system possesses local Poincare invariance and
hence belongs to Poincare gauge theory with matter. The complete Hamiltonian
analysis of the theory is carried out without gauge fixing but under certain
ansatz on the coupling parameters, which leads to a consistent connection
dynamics with second-class constraints and torsion. After performing a partial
gauge fixing, all second-class constraints can be solved, and a
SU(2)-connection dynamical formalism of the theory can be obtained. Hence, the
techniques of loop quantum gravity can be employed to quantize this Poincare
gauge theory with non-zero torsion. Moreover, the Barbero-Immirzi parameter in
loop quantum gravity acquires its physical meaning as the coupling parameter
between the Hilbert-Palatini term and the quadratic torsion term in this gauge
theory of gravity.
