
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 HilbertSchmidt 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 AharonovBohm 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 ChernSimons 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.
contact
 NITheP Stellenbosch node
 Rene Kotze
National Institute for Theoretical Physics
Private Bag X1
Matieland,
Stellenbosch, South Africa,7602  Phone: +27 (0)21 808 2653  Fax: +27 (0)218083862
 NITheP Gauteng node
 Paula Marais
Physical address: University of Witwatersrand
School of Physics
Jan Smuts Avenue
Braamfontein
JHB
 Phone: 27 (0)11 717 6898  Fax:
 NITheP KZN node
 Ms Nelisiwe Mncube
National Institute for Theoretical Physics
University of KwaZuluNatal
Private Bag x54001
Durban
4000
South Africa
 Phone: 27 (0)31 260 7570  Fax: 27 (0)31 260 8090
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