# Category:Mathematical quantization

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Here is a list of articles in the category **Mathematical quantization** of the Physics portal. In physics, **mathematical quantization** applies abstract mathematical formulations to describe the process of quantizing classical Hamiltonian and Lagrangian^{[disambiguation needed]} systems, and in particular, quantizing line bundles that are defined on symplectic manifolds. Mathematical quantization uses the modern mathematics techniques of differential geometry to accomplish this task.
A different but related approach to quantization in noncommutative mathematics, which is not based on Hamiltonian mechanics, is seen through the quantization of algebraic groups, such as by Hopf algebras, the Virasoro algebra and the Kac–Moody algebra. The result of quantization leads to the study of noncommutative geometry whereby Connes emphasized C*-algebras.

A version of quantization for functions is q-analogs.

## Pages in category "Mathematical quantization"

The following 26 pages are in this category, out of 26 total.

### C

- Canonical quantization
*(physics)*

### D

- Dirac bracket
*(physics)* - Dirac–von Neumann axioms
*(physics)*

### F

- Fredholm module
*(computing)* - Fuzzy sphere
*(computing)*

### G

- Geometric quantization
*(computing)*

### H

- Heisenberg group
*(computing)*

### K

- Kontsevich quantization formula
*(physics)*

### L

- Lagrangian foliation
*(computing)* - Lagrangian Grassmannian
*(computing)*

### M

- Moyal bracket
*(physics)* - Moyal product
*(computing)*

### N

- Noncommutative geometry
*(computing)* - Noncommutative quantum field theory
*(physics)*

### P

- Phase-space formulation
*(physics)*

### Q

- QED vacuum
*(physics)* - Quantization
*(physics)* - Quantization commutes with reduction
*(physics)* - Quantization of the electromagnetic field
*(physics)* - Quantum affine algebra
*(computing)* - Quantum enveloping algebra
*(computing)* - Quantum group
*(computing)*

### S

- Second quantization
*(physics)* - Stone–von Neumann theorem
*(computing)*

### T

- Theta representation
*(computing)*

### W

- Wigner–Weyl transform
*(physics)*