  Dirac's leaping insight that the normalized anti-commutator of the
{\gamma}^{\mu} matrices must equal the timespace signature {\eta}^{\mu}{\nu}
was decisive for the success of his equation. The {\gamma}^{\mu}-s are the same
in all Lorentz frames and "describe some new degrees of freedom, belonging to
some internal motion in the electron". Therefore, the imposed link to
{\eta}^{\mu}{\nu} constitutes a separate postulate of Dirac's theory. I derive
a manifestly covariant first order equation from the direct quantization of the
classical 4-momentum vector using the formalism of Geometric Algebra. All
properties of the Dirac electron & positron follow from the equation -
preconceived 'internal degrees of freedom', ad hoc imposed signature and
matrices unneeded. In the novel scheme, the Dirac operator is frame-free and
manifestly Lorentz invariant. Relative to a Lorentz frame, the classical
spacetime frame vectors e^{\mu} appear instead of the {\gamma}^{\mu} matrices.
Axial frame vectors (without cross product) of the 3D orientation space
defining spin and rotations appear instead of the Pauli matrices; polar frame
vectors of the 3D position space naturally define boosts, etc. Not the least,
the formalism shows a significantly higher computational efficiency compared to
matrices.
