Consider the mechanics of point-like particles. How would we shift from modeling them [classically](Mechanics%20(index).md) to modeling them as [quantum mechanical objects](Quantum%20Mechanics%20(index).md)? We do this with the following quantization procedure: 1. redefining a measurable quantity in your theory as an [observable](Observable.md) ^47eb76 2. Imposing a [commutation relation](Commutators%20in%20quantum%20mechanics.md#Commuting%20and%20non-commuting%20pairs%20of%20observables) relating it to a [conjugate variable.](conjugate%20observables%20in%20quantum%20mechanics.md) [Step 1.](Quantization#^47eb76) may be justified by considering that the [correspondence principle](Correspondence%20Principle.md) tells us that classical and quantum mechanical results converge at large scales. So, one may reason also that we may at small scales models that may be otherwise modeled classically exhibit quantization. In addition we may also may view the commutator as a modified [Poisson bracket](Poisson%20bracket.md) such that  %%Derive this relationship more completely. That will probably get its own subsection. See also pg 17 of _Quantum Gravity From Theory to Experimental Search_ in order to see where this breaks down. This relationship is from Dirac's textbook Principles of Quantum Mechanics. Use that as well.%% # Constraints to quantization ## The Groenewold-van Hove no-go theorem The _Groenwold-van Hove no-go theorem_ prevents us from [quantizing](Quantization.md) measurable quantities expressed as polynomials with a degree greater than 2. ([...see more](Groenewold-van%20Hove%20no-go%20theorem)) # Field Quantization The [above quantization procedure](Quantization.md) fact referrs to the quantization of a $(0+1)$ dimensional [field quantization](Field%20Quantization.md). ([... see more](Field%20Quantization.md)) #QuantumMechanics/FoundationsOfQuantumMechanics