Intrinsic Spinor Techniques with Applications to the Lorentz Group and the Dirac Equation

Abstract

An intrinsic spinor formalism is developed by extending the axiomatic approach of a previous paper [J. Math. Phys. 9, 284 (1968)] in which abstract tensor techniques in Minkowski space were discussed. Comparable notational and calculational advantages are achieved, and, in particular, the cumbersome spinor indices are not required. The advantages and practicality of the method are evidenced in a discussion of the Dirac equation and a novel derivation of the two- and four-dimensional spinor representations of the homogeneous Lorentz group.