Quantum Groups and Polymer Quantum Mechanics
High Energy Physics - Theory
2021-11-10 v1 General Relativity and Quantum Cosmology
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.
Cite
@article{arxiv.2105.14792,
title = {Quantum Groups and Polymer Quantum Mechanics},
author = {Giovanni Acquaviva and Alfredo Iorio and Luca Smaldone},
journal= {arXiv preprint arXiv:2105.14792},
year = {2021}
}