Minimal and nonminimal gravitational interactions,and the asymmetric energy momentum tensor

Minimal and nonminimal gravitational couplings are discussed in terms of the translation gauge fields b _k , which are necessary to describe the gravitational interaction of the spin 1/2 field. For this purpose we carry out the extension of the conventional tetrad formalism of general relativity. Our general framework contains four arbitrary parameters; one of them represents the asymmetry of the affine connection (or equivalently that of the energymomentum tensor) and the others measure possible deviations from Einstein's gravitational Lagrangian, which will be responsible for spin effects. We also discuss the physical meaning of the invariance requirement with respect to the Poincaré gauge transformation that uniquely leads us within the present framework to Einstein's theory of gravity.An abridged version of the present paper was presented at the 6th International Conference on Gravitation and Relativity at Copenhagen, July 1972.Y. Nishina Memorial Foundation Fellow, on leave of absence from the University of Tokyo, Japan.