  We retreat the well-known Einstein-Cartan theory by slightly modifying the
covariant derivative of spinor field by investigating double cover of the
Lorentz group. We first write the Lagrangian consisting of the Einstein-Hilbert
term, Dirac term and a scalar field term in a non-Riemannian spacetime with
curvature and torsion. Then by solving the affine connection analytically we
reformulate the theory in the Riemannian spacetime in a self-consistent way.
Finally we discuss our results and give future perspectives on the subject.
