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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
physics and astronomy
Path-integral action of a particle in the noncommutative plane
Physical Review Letters, Volume 102, No. 24, Article 241602, Year 2009
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Description
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.
Authors & Co-Authors
Gangopadhyay, Sunandan
South Africa, Stellenbosch
National Institute for Theoretical Physics Nithep
India, Kolkata
West Bengal State University
Scholtz, Frederik G.
South Africa, Stellenbosch
National Institute for Theoretical Physics Nithep
South Africa, Stellenbosch
Stellenbosch University
Statistics
Citations: 54
Authors: 2
Affiliations: 3
Identifiers
Doi:
10.1103/PhysRevLett.102.241602
ISSN:
00319007
e-ISSN:
10797114