Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

Abstract

We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a $\theta$-modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the $\theta$-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (à la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the $\theta$-modified Pauli equation. Then, we extract $\theta$-modified interaction between a nonrelativistic spin and a magnetic field from the $\theta$-modified Pauli equation and construct a $\theta$-modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal EPR (Einstein-Podolsky-Rosen) states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity.

This paper has been substituted by the recent one arxiv:1008.4890

References in corpus (5)

• Dirac Equation in Noncommutative Space for Hydrogen Atom
• Magnetic fields in noncommutative quantum mechanics
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Two interacting spins in external fields. Four-level systems
• Four-level systems and a universal quantum gate

Cited by in corpus (5)

• Classical Noncommutative Electrodynamics with External Source
• Noncommutative magnetic moment of charged particles
• Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon
• Noncommutative Landau problem in graphene: a gauge-invariant analysis with the Seiberg-Witten map
• Zitterbewegung in Noncommutative Geometry