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Showing posts from March, 2022

Canonical (anti)commutation relations from the path integral

I like the path integral. The question of whether the path integral or canonical quantization is "more fundamental" is purely ideological, and impossible to answer. On the one hand, canonical quantization is rigorously defined in a much wider setting than the path integral; on the other hand, canonical quantization introduces "order ambiguities" in quantizing certain operators, and requires renormalization to define operators like $\phi(0)^2,$ while both of these issues are automatically avoided in the path integral. These advantages make me, personally, a path integral devotee. One big advantage of canonical quantization over the path integral, however, is that it automatically gives you the canonical (anti)commutation relations between field operators and their conjugate momenta; in fact, this is basically the definition of canonical quantization: it gives a prescription for defining canonical (anti)commutators in terms of a bracket on the phase space of the clas