advanced_tools:quantization
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advanced_tools:quantization [2018/05/05 16:59] jakobadmin [Intuitive] |
advanced_tools:quantization [2022/06/12 06:02] (current) 192.154.255.53 [Intuitive] |
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| - | 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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| 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 |}} | + | {{ :advanced_tools:quantizationnot.png?nolink&400 |}} |
| {{ :advanced_tools:quantization-box.png?nolink&400|}} | {{ :advanced_tools:quantization-box.png?nolink&400|}} | ||
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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> | ||
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| <blockquote> | <blockquote> | ||
advanced_tools/quantization.1525532344.txt.gz · Last modified: 2018/05/05 14:59 (external edit)
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