This paper employs the ideas of geometric algebra to investigate the physical content of Dirac’s electron theory. The basis is Hestenes’ discovery of the geometric significance of the Dirac spinor, which now represents a Lorentz transformation in spacetime. This transformation specifies a definite velocity, which might be interpreted as that of a real electron. Taken literally, this velocity yields predictions of tunnelling times through potential barriers, and defines streamlines in spacetime that would correspond to electron paths. We also present a general, first-order diffraction theory for electromagnetic and Dirac waves. We conclude with a critical appraisal of the Dirac theory.
S. F. Gull, A. N. Lasenby and C. J. L. Doran, Electron Paths, Tunnelling and Diffraction in the Spacetime Algebra, Found. Phys. 23(10), 1329-1356 (1993)