Phase space quantization and Loop Quantum Cosmology: A Wigner function for the Bohr-compactified real line

Details Phase space quantization and Loop Quantum Cosmology: A Wigner function for the Bohr-compactified real line Phase space quantization and Loop Quantum Cosmology: A Wigner function for the Bohr-compactified real line

2008-04-16

arxiv.org/abs/0804.2541v1

Class.Quant.Grav.25:225015,2008

Physics

Mathematical Physics

26 pages, 3 figures

Scientific paper

10.1088/0264-9381/25/22/225015

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.

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