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advanced_tools:quantization [2018/05/05 14:03]
63.143.42.253 ↷ Links adapted because of a move operation
advanced_tools:quantization [2022/06/12 06:02] (current)
192.154.255.53 [Intuitive]
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 <tabbox Intuitive> ​ <tabbox Intuitive> ​
-Quantization ​is a phenomenon where the constraints of the physical system have the effect that some physical quantity only appears in discrete jumps, while all values in between physically forbidden. ​+Sometimes when people talk about ``quantization",​ what they really mean is //​discretization//,​ i.e., a phenomenon where the constraints of the physical system have the effect that some physical quantity only appears in discrete jumps, while all values in between ​are physically forbidden. ​
  
 The easiest example is a rope that is held under constant tension by two hands: The easiest example is a rope that is held under constant tension by two hands:
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-{{ :​advanced_tools:​quantization-box.png?​nolink&​400|}} 
  
-The thing is, no matter how the two hands try to make the rope vibrate, the rope will only vibrate with a quantized set of modes. The two hands fix the rope at both ends. As a result of this constraint, the rope can only vibrate with fixed frequencies. The frequencies between this fixed set of frequencies are physically impossible. ​+ 
 +The thing is, no matter how the two hands try to make the rope vibrate, the rope will only vibrate with a quantized set of modes. The two hands fix the rope at both ends. As a result of this constraint, the rope can only vibrate with fixed frequencies. The frequencies between this fixed set of frequencies are physically impossible
 + 
 +{{ :​advanced_tools:​quantizationnot.png?​nolink&​400 |}} 
 + 
 +{{ :​advanced_tools:​quantization-box.png?​nolink&​400|}}
  
 The same thing now happens also in [[theories:​quantum_mechanics|quantum mechanics]]. ​ The same thing now happens also in [[theories:​quantum_mechanics|quantum mechanics]]. ​
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-A nice summary can be found in [[https://​arxiv.org/​abs/​math-ph/​0405065|Quantization Methods: A Guide for Physicists and Analysts]] by S. Twareque Ali, Miroslav Engliš. See also [[https://​arxiv.org/​abs/​math-ph/​9809011|Obstructions to Quantization]] by Mark J. Gotay and Landsman, N.P.: Mathematical topics between classical and quantum mechanics. Springer Monographs in Mathematics. Springer-Verlag,​ New York, 1998.+  * A nice summary can be found in [[https://​arxiv.org/​abs/​math-ph/​0405065|Quantization Methods: A Guide for Physicists and Analysts]] by S. Twareque Ali, Miroslav Engliš. 
 +  *  ​See also [[https://​arxiv.org/​abs/​math-ph/​9809011|Obstructions to Quantization]] by Mark J. Gotay and Landsman, N.P.: Mathematical topics between classical and quantum mechanics. Springer Monographs in Mathematics. Springer-Verlag,​ New York, 1998. 
 +  * and the book Quantization of Gauge Systems by Henneaux and Teitelboim
  
 -->​Canonical Quantization#​ -->​Canonical Quantization#​
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 ---- ----
 +
 +<​blockquote>​Quantization is an art form which, when applied to classical physical theories, yields predictions of subatomic behavior which are in spectacular agreement with experiments.
 +<​cite>​[[https://​arxiv.org/​abs/​alg-geom/​9705010|Ron Y. Donagi]]</​cite>​
 +</​blockquote>​
 +
  
 <​blockquote>​ <​blockquote>​
advanced_tools/quantization.1525521835.txt.gz · Last modified: 2018/05/05 12:03 (external edit)