Path integral action of a particle in a magnetic field in the noncommutative plane and the Aharonov-Bohm effect

Abstract

The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a particle moving in the noncommutative plane and in the presence of a magnetic field and an arbitrary potential. Using this action, the equation of motion and the ground state energy for the partcle are obtained explicitly. The Aharonov-Bohm phase is derived using a variety of methods and several dualities between this system and other commutative and noncommutative systems are demonstrated. Finally, the equivalence of the path integral formulation with the noncommutative Schrödinger equation is also established.

12 pages Latex, References added, To appear in J.Phys.A

References in corpus (5)

• Formulation, Interpretation and Application of non-Commutative Quantum Mechanics
• Path integral action of a particle in the non commutative plane
• Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect
• Noncommutative quantum mechanics -- a perspective on structure and spatial extent
• A coherent-state-based path integral for quantum mechanics on the Moyal plane

Cited by in corpus (3)

• Thermodynamics of a charged particle in a noncommutative plane in a background magnetic field
• Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves
• Non-commutativity from exact renormalization group dualities