  In contrast to formulations of the Dirac theory by Hestenes and by the
current author, the formulation recently presented by W. P. Joyce [J. Phys. A:
Math. Gen. 34 (2001) 1991--2005] is equivalent to the usual Dirac equation only
in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation
can be solutions either of the Dirac equation in the Hestenes form or of the
same equation with the sign of the mass reversed, and in general they are
mixtures of the two possibilities. Because of this relationship, Joyce obtains
twice as many linearly independent plane-wave solutions for a given momentum
eigenvalue as exist in the conventional theory. A misconception about the
symmetry of the Hestenes equation and the geometric significance of the
algebraic spinors is also briefly discussed.
