Comments on "Dirac theory in spacetime algebra"

Details Comments on "Dirac theory in spacetime algebra" Comments on "Dirac theory in spacetime algebra"

2002-02-11

arxiv.org/abs/quant-ph/0202060v1

Physics

Quantum Physics

7 pages, accepted for publication inJournal of Physics A: Mathematical and General on 11 Feb 2002 as Comment

Scientific paper

10.1088/0305-4470/35/22/401

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.

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