About: Generally covariant quantum mechanics on noncommutative configuration spaces

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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)
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)
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)
skos:notation	RIV/47813059:19610/07:#0000195!RIV08-MSM-19610___
http://linked.open.../vavai/riv/strany	112101-1;112101-15
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA202/05/2767), Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	11
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Kopf, Tomáš
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	423077
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/07:#0000195
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	quantum mechanics; general covariance; noncommutative geometry (en)
http://linked.open.../riv/klicoveSlovo	quantum mechanics general covariance noncommutative geometry
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[F05D1B3B61C0]
http://linked.open...i/riv/nazevZdroje	Journal of Mathematical Physics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Generally covariant quantum field theory and noncommutative geometry
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	48
http://linked.open...iv/tvurceVysledku	Kopf, Tomáš Paschke, Mario
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	0022-2488
number of pages	15 (xsd:int)
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	Generally covariant quantum mechanics on noncommutative configuration spaces Generally covariant quantum mechanics on noncommutative configuration spaces Generally covariant quantum mechanics on noncommutative configuration spaces

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