  Reformulation of the Dirac equation in terms of the real Spacetime Algebra
(STA) reveals hidden geometric structure, including a geometric role for the
unit imaginary as generator of rotations in a spacelike plane. The STA and the
real Dirac equation play essential roles in a new Gauge Theory Gravity (GTG)
version of General Relativity (GR). Besides clarifying the conceptual
foundations of GR and facilitating complex computations, GTG opens up new
possibilities for a unified gauge theory of gravity and quantum mechanics,
including spacetime geometry of electroweak interactions. The Weinberg-Salam
model fits perfectly into this geometric framework, and a promising variant
that replaces chiral states with Majorana states is formulated to incorporate
zitterbewegung in electron states.
