Two-Component Poincaré-Invariant Equations for Massive Charged Leptons

Abstract

An alternative to Dirac's factorization of the Klein-Gordon equation is developed; the resulting two-component, $m\ne 0$ equations are proved Poincaré invariant. The particles interact chirally and minimally with the electromagnetic field ($g=2\mathrm{}$). Our equations yield factorizations of Kramers's equations and a conserved chiral current (without ${\gamma }_5$ projection) to implement in a natural way the Feynman—Gell—Mann approach to weak interactions. Besides possessing sharp chirality, the particles possess a new dichotomic quantum number.