Conceptual aspects of non-positive quantization

We draw a distinction between 'positive' and 'non-positive' quantization schemes. Although the former are somewhat known to philosophers (in both canonical and path integral versions), the latter are almost entirely unstudied in the philosophy literature; moreover, physics writings on non-positive quantization often proceed in a manner which is not maximally systematic. As such, this paper aims both to introduce to philosophers the powerful tools of non-positive quantization schemes and their applications and to provide a systematic lay-of-the-land for such approaches which should be of value to philosophers and physicists alike.