Dirac Equations and Einstein Theory

Abstract

HERMANN WEYL (Proc. Nat. Acad. of the U.S.A., 15, 323; April 1929) has recently developed a relativistic theory of the Dirac equation which, like that of Wigner (Zeit. f. Phys., 53, 592; 1929), and that of Vallarta and myself (NATURE, Mar. 2, 1929, p. 317), employs the Einstein notion of an ‘n-leg’. Unlike the two other theories, Weyl rejects Einstein's distant parallelism, and obtains a theory invariant under a local rotation varying continuously from point to point. That is, Weyl's theory depends solely on the gλµ's of Einstein's 1916 gravitational theory, and not on the ^shλ of his 1929 theory. It is perhaps interesting to remark that the same degree of invariance may be obtained by choosing as the 4-legs of the Einstein theory the Ricci principal directions. If we write R—µ for the 1916 contracted curvature tensor, this additional condition is expressed by the formula