Path-integral action of a particle in the noncommutative phase-space

Author： Gangopadhyay Sunandan Halder Aslam

E-ISSN： 1286-4854|117|1|10010-10010

ISSN： 0295-5075

Source： EPL (EUROPHYSICS LETTERS), Vol.117, Iss.1, 2017-03, pp. : 10010-10010

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Abstract

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.