Dirac theory in spacetime algebra: I. The generalized bivector Dirac equation

This paper formulates the standard Dirac theory without resorting to spinor fields. Spinor fields mix bivectors and vectors which have different prope rties in spacetime algebra. Instead the Dirac held is formulated as a gener alized bivector field. All the usual results of the standard Dirac theory f all out naturally and simply. The plane-wave solutions to the Dirac equatio n are given and found to give eight independent solutions. The solutions co rrespond to particle/antiparticle energy states, spin +/- 1/2 along the dir ection of propagation and two degrees of transverse polarization. Each solu tion has a double degeneracy corresponding to an internal U(1) circle times SU(2) symmetry of the Dirac equation. One further advantage of this formal ism is that it is completely formulated without using a matrix representati on of Clifford algebra instead of utilizing the inherent geometric meaning of the algebra.