2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/203395We give a definition for the Wigner function for quantum mechanics on the Bohr compactification of the real line and prove a number of simple consequences of this definition. We then discuss how this formalism can be applied to loop quantum cosmology. As an example, we use the Wigner function to give a new quantization of an important building block of the Hamiltonian constraint.26 pages, 3 figuresMathematical PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theory81S30text