Formulation, Interpretation and Application of Non Commutative Quantum Mechanics

by Prof. Frederik Scholtz (Director of the National Institute for Theoretical Physics (NITheP, South Africa), Department of Physics, University of Stellenbosch (South Africa))

Thursday 10 Dec 2009, 16:00 → 17:15 Europe/Brussels

E.349

In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non commutative configuration space. It is argued that the standard quantum mechanical interpretation, based on Positive Operator Valued Measures, provides a sufficient framework for the consistent interpretation of this quantum system. The formalism is applied to the harmonic oscillator and non commutative well in two dimensions. The path integral action for a particle moving in a two dimensional non commutative plane is also derived. The possible physical signatures of non commutativity are identified and briefly discussed.