Lorentz-invariant spin-½ equation for the representation (1,½) ⊕ (½,0) ⊕ (0,½) ⊕ (½,1)

Abstract

A new class of Lorentz-invariant equations for a particle of unique mass m and spin 1/2 and corresponding to the Lorentz-group representation (1,1/2) direct-sum (0,1/2) direct-sum (1/2,0) direct-sum (1/2,1) is derived. These equations are irreducible and are obtainable from a Lagrangian. The g factor is found to be 2/3+(4/3) vertical-bar1-2f vertical-bar/sup 2/, where f is an arbitrary nonzero complex parameter. Although the total charge is positive definite in the free-field case, thereby allowing consistent second quantization, the minimally coupled field exhibits the problems of the indefinite metric.