Putting positrons into classical Dirac field theory

One way of arriving at a quantum field theory of electrons and positrons is to take a classical theory of the Dirac field and then quantize. Starting with the standard classical field theory and quantizing in the most straightforward way yields an inadequate quantum field theory. It is possible to fix this theory by making some modifications (such as redefining the operators for energy and charge). Here I argue that we ought to make these modifications earlier, revising the classical Dirac field theory that serves as the starting point for quantization (putting positrons into that theory and removing negative energies). Then, quantization becomes straightforward. Also, the physics of the Dirac field is made more similar to the physics of the electromagnetic field and we are able to better understand electron spin.