The spatial wavefunction of half-integer spins

Within a nonrelativistic framework, spin is generally included as an intrinsic angular momentum. It is proposed here that consistent results can be obtained with a spatial wavefunction of an oriented complex exponential e(-/+ i (a) over cap phi) , where the bivector i (a) over cap is written in terms of the pseudoscalar i = e(x)e(y)e(z) and the axis of rotation given by the unit vector (a) over cap, which is generally an (effective) magnetic field direction (this can also be written as e(-/+ i (a) over cap phi) in terms of the Pauli vector sigma). The wavefunction is a multivector and not a complex scalar. The signs in the exponential correspond to the two directions of rotation around the axis. The transformation properties of these wavefunctions are given by the Pauli spinors. Spin can be viewed as a zero-point rotation arising from the noncommutativity of the momentum and the vector potential.