On the relations of the tensor-calculus to the spinor-calculus

Abstract

In this paper it is first shown (2) that a six-vector which has the property of being identical with its own dual six-vector, and which, moreover, has its invariant null, has properties equivalent to those of a spinor. It is then shown (3) that the correspondence thus set up between tensor-analysis and spinor-analysis enables us to replace some complicated tensor-operations by simple spinor-operations. In 4 the correspondence is applied to the tensorization of Dirac’s relativistic equation of the electron, in connexion with its generalization to the space-time of general relativity. It is shown that Dirac’s equations are equivalent to the vanishing of an ordinary vector.