On Poisson brackets and symplectic structures for the classical and quantum zitterbewegung

The symplectic structures (brackets, Hamilton's equations, and Lagrange's equations) for the Dirac electron and its classical model have exactly the same form. We give explicitly the Poisson brackets in the dynamical variables (x ,p ,v ,S ^v). The only difference is in the normalization of the Dirac velocities =4 which has significant consequences.Dedicated to David Hestenes, whose work profoundly connects geometry (spacetime), algebra (Clifford), and physics (electron).