Quantum Particle on a Quantum Circle

Abstract

We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.

11 pages, LaTeX

Cited by in corpus (7)

• q-Deformed Conformal Quantum Mechanics
• Coherent state quantization of a particle in de Sitter space
• Simple model of big-crunch/big-bang transition
• Dynamics in a noncommutative phase space
• Wick ordering for coherent state quantization in 1+1 de Sitter space
• Coherent states for the q-deformed quantum mechanics on a circle
• Quantum mechanics on a circle with a finite number of α-uniformly distributed points