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There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X $X$ is some X_hbar $X_\hbar$ depending on a parameter hbar $\hbar$ (occasionally q=e^hbar $q=e^\hbar$ instead) such that X=X_0 $X=X_0$ and X_hbar $X_\hbar$ is generically "less commutative" than X. $X$. This is by analogy with quantum physics where X_0 $X_0$ is classical physics and hbar $\hbar$ measures the failure of position and momentum to commute.

2 edited body; added 1 characters in body

There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X is some X_hbar depending on a parameter hbar (ocassionaly occasionally q=e^hbar instead) such that X=X_0 and X_hbar is generically "less commutative" than X. This is by analogy with quantum physics where X_0 is classical physics and hbar measures the failure of position and momentum to commute.

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There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X is some X_hbar depending on a parameter hbar (ocassionaly q=e^hbar instead) such that X=X_0 and X_hbar is generically "less commutative" than X. This is by analogy with quantum physics where X_0 is classical physics and hbar measures the failure of position and momentum to commute.