By Hestenes D.
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The velocity v(x) defines a local reference frame at x called the electron rest frame. The proper probability density ρ = (ρv) · v can be interpreted as the probability density in the rest frame. 3) implies that through each spacetime point there passes a unique integral curve which is tangent to v at each of its points. Let us call these curves (electron) streamlines. In any spacetime region where ρ = 0, a solution of the Dirac equation determines a family of streamlines which fills the region with exactly one streamline through each point.
There are other ways to represent a Dirac spinor in the STA,12 but all representations are, of course, mathematically equivalent. The representation chosen here has the advantages of simplicity and, as we shall see, ease of interpretation. To distinguish a spinor ψ in the STA from its matrix representation Ψ in the Dirac algebra, let us call it a real spinor to emphasize the elimination of the ungeometrical imaginary i . Alternatively, we might refer to ψ as the operator representation of a Dirac spinor, because, as shown below, it plays the role of an operator generating observables in the theory.
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