The Dirac equation for accountants

In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schrödinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics.