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Description
| - We generalize the previously given algebraic version of %22Feynman's proof of Maxwell's equations%22 to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., of nonabelian Yang-Mills theories, and of noncommutative tori. Moreover we, examine models over the Moyal-deformed plane. Assuming the conservation of electrical charges, we show that in this case the canonical uncertainty relation [x_k, \dot{x}_l] = ig_{kl} with metric g_{kl} is only consistent if g_{kl} is constant.
- We generalize the previously given algebraic version of %22Feynman's proof of Maxwell's equations%22 to noncommutative configuration spaces. By doing so, we also obtain an axiomatic formulation of nonrelativistic quantum mechanics over such spaces, which, in contrast to most examples discussed in the literature, does not rely on a distinguished set of coordinates. We give a detailed account of several examples, e.g., of nonabelian Yang-Mills theories, and of noncommutative tori. Moreover we, examine models over the Moyal-deformed plane. Assuming the conservation of electrical charges, we show that in this case the canonical uncertainty relation [x_k, \dot{x}_l] = ig_{kl} with metric g_{kl} is only consistent if g_{kl} is constant. (en)
- Zobecňujeme dříve vypracovanou algebraickou verzi %22Feynmanova důkazu Maxwellových rovnic%22 na nekomutativní prostory. Přitom obdržíme axiomatickou formulaci nerelativistické kvantové mechaniky na takovýchto prostorech, která se, na rozdíl od většiny příkladů diskutovaných v literatuře, neopírá o zvolené souřadnice. Podrobně probíráme několik příkladů, např. neabelovské Yangovy-Millsovy teorie a nekomutativní torus. Navíc zkoumáme modely nad moyalovsky deformovanou rovinou. Za předpokladu zachování elektrického náboje ukážeme, že v tomto případě kanonické komutační relace [x_k, \dot{x}_l] = ig_{kl} s metrikou g_{kl} jsou konsistentní pouze, pokud g_{kl} je konstantní. (cs)
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Title
| - Generally covariant quantum mechanics on noncommutative configuration spaces
- Obecně kovariantní kvantová mechanika na nekomutativních konfiguračních prostorech (cs)
- Generally covariant quantum mechanics on noncommutative configuration spaces (en)
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skos:prefLabel
| - Generally covariant quantum mechanics on noncommutative configuration spaces
- Obecně kovariantní kvantová mechanika na nekomutativních konfiguračních prostorech (cs)
- Generally covariant quantum mechanics on noncommutative configuration spaces (en)
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skos:notation
| - RIV/47813059:19610/07:#0000195!RIV08-MSM-19610___
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA202/05/2767), Z(MSM4781305904)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/47813059:19610/07:#0000195
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - quantum mechanics; general covariance; noncommutative geometry (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Journal of Mathematical Physics
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
| - Kopf, Tomáš
- Paschke, Mario
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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is http://linked.open...avai/riv/vysledek
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