Volume 117, Number 1, January 2017
|Number of page(s)||5|
|Published online||28 February 2017|
Path-integral action of a particle in the noncommutative phase-space
1 Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata Mohanpur 741246, Nadia, West Bengal, India
2 Inter University Centre for Astronomy & Astrophysics (IUCAA) - Pune, India
3 Kolorah H.A.W. Institution - Kolorah, Howrah 711411, India
Received: 18 December 2016
Accepted: 8 February 2017
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum system in the space of Hilbert-Schmidt operators acting on noncommutative configuration space, the path integral action of a particle is derived. It is observed that the action has a similar form to that of a particle in a magnetic field in the noncommutative plane. From this action the energy spectrum is obtained for the free particle and the harmonic-oscillator potential. We also show that the nonlocal nature (in time) of the action yields a second-class constrained system from which the noncommutative Heisenberg algebra can be recovered.
PACS: 04.60.Bc – Phenomenology of quantum gravity / 03.65.-w – Quantum mechanics
© EPLA, 2017
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