Some Considerations on a Nonlinear Field Theory

Abstract

The question is investigated whether the only one spinor field is sufficient to describe all the elementary particles and their interactions (including the gravitational interactions) spinor-unified·field-theoretically. First it turns out that it is impossible to compose the fundamental metric tensor gp.v out of .p. This leads us to stand on the dualism of gravitational field and matter fields. Second, it is suggested that the spin affine connection r~' in the general Dirac equation has a possibility of involving rather uniquely the fundamental strong and weak interaction terms as well as the electromagnetic interaction term. Third, it is presumed, however, that it will be necessary at least three kinds (S) (W) of spinor fields, .p, .p (both four components) and X (two components) in order to describe various kinds of elementary particles, based on a considera· tion about the weak interaction term, and on the empirical fact that there exist those elementary particles which have no strong interaction, as well as on the condition that the field equations should be derived from a variation principle. Thus a set of field equations is proposed. §