  In general relativity the fermions are treated from the perspective of the
gauged Lorentz group and by introducing the corresponding gauge fields the spin
connection. This procedure is intimately related to the so-called "vielbein"
formalism and stems from the general structure that can be associated to a
manifold, the affine connection. In this work we derive the correct spin
connection based only on the general covariance of the theory, on the gauged
Lorentz symmetry and on the known space-time properties of fermion bilinears
generalized to the curved space. Our result coincides exactly with the spin
connection obtain through the tetrad formalism.

General Relativity and Quantum Cosmology;High Energy Physics - Theory