A classification of finite quantum kinematics

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F14%3A00225927" target="_blank" >RIV/68407700:21340/14:00225927 - isvavai.cz</a>

Výsledek na webu

<a href="http://iopscience.iop.org/1742-6596/538/1/012020" target="_blank" >http://iopscience.iop.org/1742-6596/538/1/012020</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1742-6596/538/1/012020" target="_blank" >10.1088/1742-6596/538/1/012020</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A classification of finite quantum kinematics

Popis výsledku v původním jazyce

Quantum mechanics in Hilbert spaces of finite dimension N is reviewed from the number theoretic point of view. For composite numbers N possible quantum kinematics are classified on the basis of Mackey's Imprimitivity Theorem for finite Abelian groups. This yields also a classification of finite Weyl-Heisenberg groups and the corresponding finite quantum kinematics. Simple number theory gets involved through the fundamental theorem describing all finite discrete Abelian groups of order N as direct products of cyclic groups, whose orders are powers of not necessarily distinct primes contained in the prime decomposition of N. The representation theoretic approach is further compared with the algebraic approach, where the basic object is the correspondingoperator algebra. The consideration of fine gradings of this associative algebra thenbrings a fresh look on the relation between the mathematical formalism and physical realizations of finite quantum systems.

Název v anglickém jazyce

A classification of finite quantum kinematics

Popis výsledku anglicky

Quantum mechanics in Hilbert spaces of finite dimension N is reviewed from the number theoretic point of view. For composite numbers N possible quantum kinematics are classified on the basis of Mackey's Imprimitivity Theorem for finite Abelian groups. This yields also a classification of finite Weyl-Heisenberg groups and the corresponding finite quantum kinematics. Simple number theory gets involved through the fundamental theorem describing all finite discrete Abelian groups of order N as direct products of cyclic groups, whose orders are powers of not necessarily distinct primes contained in the prime decomposition of N. The representation theoretic approach is further compared with the algebraic approach, where the basic object is the correspondingoperator algebra. The consideration of fine gradings of this associative algebra thenbrings a fresh look on the relation between the mathematical formalism and physical realizations of finite quantum systems.

Druh

D - Stať ve sborníku

CEP obor

BD - Teorie informace

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Journal of Physics Conference Series

ISBN

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ISSN

1742-6588

e-ISSN

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Počet stran výsledku

12

Strana od-do

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Název nakladatele

IOP Publishing Ltd

Místo vydání

Bristol

Místo konání akce

Bregenz

Datum konání akce

21. 7. 2013

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000346163000018