Path-integral action of a particle in the noncommutative plane
Date
2009
Authors
Gangopadhyay S.
Scholtz F.G.
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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, we formulate a coherent state approach to the path-integral representation of the transition amplitude. 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. However, this nonlocality can be removed by introducing an auxilary field, which leads to a second class constrained system that yields the noncommutative Heisenberg algebra upon quantization. Using this action, the propagator of the free particle and harmonic oscillator are computed explicitly. © 2009 The American Physical Society.
Description
Keywords
Arbitrary potentials, Coherent state, Configuration space, Constrained systems, Free particles, Harmonic oscillators, Heisenberg, Hilbert-Schmidt operators, Non-commutative, Non-commutative quantum mechanics, Nonlocal, Nonlocality, Path-integral, Quantum system, Transition amplitudes, Molecular vibrations, Quantum electronics, Quantum optics, Oscillators (electronic)
Citation
Physical Review Letters
102
24
102
24