Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors

Abstract

A compatible spin 1 spinor representation with Clifford algebra (1,3) (or1,3Cl ) is derived for both(1/ 2,1/ 2) and(1, 0) (0,1) Lorentz group representations with spin 1/2 particles Dirac spinors in1,3Cl . The relation between the two different representations of spin 1 spinors is analogous to the relation between the electromagnetic vector potential fieldA and the electromagnetic field strength tensorF  . From this relationship, the two representations are combined by the formula( , ) ( , ) /u p p p m     . We also note that the Grassmann basis provides more convenient basis for spin 1 spinors especially in chiral representations of(1, 0) (0,1) , even though the Clifford basis is more fitting for spin 1/2 and(1/ 2,1/ 2) spinor representations for both helicity and handedness.