Spinor fields in the theory of relativity and a generalization of Heisenberg's nonlinear spinor equation

Abstract

Some years ago it was shown that the nonlinear term of Heisenberg's spinor equation can be derived by torsion of the Minkowski space (Cartan space). This result is applied in the investigations of this paper. As the Heisenberg equation does not show any connection with recent phenomenological theories in high energy physics, like the parton or quark model, the problems of the metric of space-time are discussed from the aspect of fundamental axioms of topology (Hausdorff space). It will be shown that Feynman's relativistic parton theory can be derived by means of a quantised de Sitter space, where the constant curvature can assume only discrete values. It is also possible to derive the Dirac equation from the same mathematical considerations. A nonlinear spinor equation will be formulated which contains the parton theory and the nonlinear term of the Heisenberg equation as different approaches in the theory of elementary particles.