The electron field and the Dirac bracket

A recent quantization rule of Fermi systems starts from the new symmetric brackets of classical mechanics. As a consequence, Fermi and Bose quantization can be put on an equal footing, instead of the standardad hoc procedure. We prove that the rule gives the right anticommutation relations when applied to the case of the relativistic electron. We show that this is a crucial test of the rule.For completeness, Dirac's Hamiltonian mechanics and the plus and minus Dirac bracket formalisms are developed for the electron's field.