Quantum Mechanics is Odd

Garnet Ord

The Dirac equation in 1+1 dimension is a formal analytic continuation away from a two-component form of the classical telegraph equations. Less well-known is the fact that there is a formulation of a classical stochastic process in which the classical and quantum equations represent respectively even and odd components of classical densities. This observation leads directly to an interpretation of both equations that is in accord with the geometric algebra picture. An appealing feature of this route to the two equations is that the `abstract' representation of vectors by matrices in GA arises directly from an easily interpreted transition matrix for a Markov process.