Phase space quantization and Loop Quantum Cosmology: A Wigner function   for the Bohr-compactified real line
  We 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. 
Christopher J. Fewster, Hanno Sahlmann