GENERAL-CONSIDERATIONS OF MATTER COUPLING WITH THE SELF-DUAL CONNECTION

It has been shown for low-spin fields that the use of only the self-du al part of the connection as basic variable does not lead to extra con ditions or inconsistencies. We study whether this is true for more gen eral chiral action. We generalize the chiral gravitational action, and assume that half-integer spin fields are coupled with torsion linearl y. The equation for torsion is solved and substituted back into the ge neralized chiral action, giving four-fermion contact terms. If these c ontact terms are complex, the imaginary part will give rise to extra c onditions for the gravitational and matter field equations. We study t he four-fermion contact terms taking spin-1/2 and spin-3/2 fields as e xamples.