In physics, usually quantization means canonical quantization. i.e., which we treat classical objects to quantum operators. i.e., For the association $Q:f \mapsto \hat{f}$ from functions on the classical space of states to operators on quantum states: $$[Q(f), Q(g)] = -i\hbar Q(\{f,g\})$$ where $[-,-]$ is the commutator of linear maps and $\{-,-\}$ is the Poisson bracket.
In terms of mathematics (or mathematical physics society) the quantization can be split into three subjects:
Can anyone give me a nice explanation of the difference between three three quantizations? What are the similarities and differences between them?
Naively, I noticed quantization is related to Hamiltonian and so symplectic geometry but not have much deeper thoughts on this topic.
