• Jun 18 2014

    NITheP Stellenbosch node seminar: Prof Sunandan Gangopadhyay


    ABSTRACT: Noncommutative quantum mechanics can be viewed as a quantum system represented in the space of Hilbert-Schmidt operators acting on noncommutative configuration space. Taking this as a departure point, a coherent state approach to the path integral representation of the transition amplitude is formulated. From this we derive an action for a particle moving in the noncommutative plane and in the presence of an arbitrary potential. We find that this action is nonlocal in time.
    Using this action, the propagator of the free particle and harmonic oscillator are computed explicitly. The path integral action for a particle moving in the noncommutative plane and in the presence of a magnetic field is obtained next. The Aharonov-Bohm phase is computed from this action and involves a noncommutative correction. We then demonstrate that the path integral formalism leads to a quantum mechanics involving a Chern-Simons term in momentum which is of noncommutative origin. Finally, we show, firstly, the construction of dualities using the exact renormalization group approach and, secondly, that spatial noncommutativity can emerge as such a duality.