Quantum groups and polymer quantum mechanics

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10439641" target="_blank" >RIV/00216208:11320/21:10439641 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8gH9_9YoCS" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=8gH9_9YoCS</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0217732321502291" target="_blank" >10.1142/S0217732321502291</a>

Result language
angličtina
Original language name
Quantum groups and polymer quantum mechanics
Original language description
In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Quantum Gravity, position and momentum operators cannot be both well defined on the Hilbert space (Script capital HPoly). It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a q-oscillator structure, and hence q-deformed creation/annihilation operators, can be naturally defined on Script capital HPoly, which is then mapped into the sum of many copies of the q-oscillator Hilbert space. This shows that the q-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of Script capital HPoly is of topological nature.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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