Quantum groups and polymer quantum mechanics

In Polymer Quantum Mechanics, a quantization scheme that naturally emerges from Loop Gravity, position and momentum operators cannot be both well defined on the Hilbert space [Formula: see text]. It is henceforth deemed impossible to define standard creation annihilation operators. this paper, we show text]-oscillator structure, hence text]-deformed creation/annihilation operators, can text], which then mapped into sum of many copies space. This shows text]-calculus natural calculus for Mechanics. Moreover, inequivalence different superselected sectors text] topological nature.