Deformation Quantization and Wigner Functions

Abstract

We review the Weyl-Wigner formulation of quantum mechanics in phase space. We discuss the concept of Narcowich-Wigner spectrum and use it to state necessary and sufficient conditions for a phase space function to be a Wigner distribution. Based on this formalism we analize the modifications introduced by the presence of boundaries. Finally, we discuss the concept of environment-induced decoherence in the context of the Weyl-Wigner approach.

Talk given by the second author at the Workshop on Quantum Gravity and Noncommutative Geometry, Lusofona University, Lisbon, July 2004