Geometrical unified theory of connection fields and frame fields

A theory of connections on a principal bundle with structure group SL(4,R), the highest-dimensional simple subgroup of the Clifford algebra associated with a space-time of signature (1,-1,-1,-1), is used to interpret Dirac's equation geometrically. The proposed theory unifies Dirac's equation with the equations of gravitation and electrodynamics. The Lorentz equation of motion for charges is a consequence of the field equations when the connection reduces to a component which may be identified as the electromagnetic field. If this part of the generalized connection does not vanish, we obtain the correct expression for the electric current in terms of spinors and the correct minimal coupling in the first nonrelativistic approximation.