2021/10/19 by G. Acquaviva, Giovanni Acquaviva, Alfredo Iorio +3
Physics and Astronomy · Mathematics · #Noncommutative and Quantum Gravity Theories #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics
paper · doi:10.1142/s0217732321502291
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 [Formula: see text]. It is henceforth deemed impossible to define standard creation and annihilation operators. In this paper, we show that a [Formula: see text]-oscillator structure, and hence [Formula: see text]-deformed creation/annihilation operators, can be naturally defined on [Formula: see text], which is then mapped into the sum of many copies of the [Formula: see text]-oscillator Hilbert space. This shows that the [Formula: see text]-calculus is a natural calculus for Polymer Quantum Mechanics. Moreover, we show that the inequivalence of different superselected sectors of [Formula: see text] is of topological nature.