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:

1. Deformation quantization,

2. Batalin-Vilkovisky (BV) formalism, and

3. Geometric quantization.

Can anyone give me a nice explanation of the difference between this three quantization? What are the similarity 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.

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:

1. Deformation quantization,

2. Batalin-Vilkovisky (BV) formalism, and

3. Geometric quantization.

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.

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  : (1) Deformation quantization, (2) BV formalism, and (3) Geometric quantization.

Can anyone give me a nice explanation of the difference between this three quantization? What are the similarity 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. Any comments or nice introductory reference are welcome.

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:

1. Deformation quantization,

2. Batalin-Vilkovisky (BV) formalism, and

3. Geometric quantization.

Can anyone give me a nice explanation of the difference between this three quantization? What are the similarity 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.