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arXiv · 2105.14792

Quantum Groups and Polymer Quantum Mechanics

Giovanni Acquaviva·Alfredo Iorio·Luca Smaldone
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Abstract

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 ( H_Poly ). It is henceforth deemed impossible to define standard creation and annihilation operators. In this letter we show that a q-oscillator structure, and hence q-deformed creation/annihilation operators, can be naturally defined on H_Poly , 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 H Poly is of topological nature.

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Giovanni Acquaviva, Alfredo Iorio, Luca Smaldone. 2021-05-31. Quantum Groups and Polymer Quantum Mechanics. https://doi.org/10.1142/s0217732321502291

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