A classification of finite quantum kinematics

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
A classification of finite quantum kinematics
Original language description
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.
Czech name
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Czech description
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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