Indefinite charge for the classical spinor field

A conserved Lorentz vector is defined for a two-component spinor field that obeys the Klein-Gordon equation and it is interpreted as a charge-current density. The corresponding total charge can take negative as well as positive values, which is not the case for the usual charge of the Dirac field. Consequently probability amplitudes can be defined for a relativistic quantum mechanics; and the inhomogeneous equation is solved by means of the causal Green function. This vector is not invariant under gauge transformations of the spinor field, and the equation cannot be generalized by the gauge invariant substitution to obtain the interaction with an electromagnetic field. In the limit of a massless field that obeys the Weyl equation, the charge vanishes. (author)