Path-Integral Action of a Particle in the Noncommutative Plane

Journal Article · Fri Jun 19 00:00:00 EDT 2009 · Physical Review Letters

DOI:https://doi.org/10.1103/PHYSREVLETT.102.241602· OSTI ID:21346967

Gangopadhyay, Sunandan ^[1]; Scholtz, Frederik G ^[1]

---

1. National Institute for Theoretical Physics (NITheP), Stellenbosch 7600 (South Africa)

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.

• OSTI ID: 21346967
• Journal Information: Physical Review Letters, Vol. 102, Issue 24; Other Information: DOI: 10.1103/PhysRevLett.102.241602; (c) 2009 The American Physical Society; ISSN 0031-9007
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
ANNIHILATION OPERATORS
COMMUTATION RELATIONS
EIGENSTATES
HARMONIC OSCILLATORS
PATH INTEGRALS
POTENTIALS
PROPAGATOR
QUANTIZATION
QUANTUM MECHANICS
TRANSITION AMPLITUDES
AMPLITUDES
INTEGRALS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
QUANTUM OPERATORS