Magnetic-Dipole Spin Effects in Noncommutative Quantum Mechanics

Abstract

A general three-dimensional noncommutative quantum mechanical system mixing spatial and spin degrees of freedom is proposed. The analogous of the harmonic oscillator in this description contains a magnetic dipole interaction and the ground state is explicitly computed and we show that it is infinitely degenerated and implying a spontaneous symmetry breaking. The model can be straightforwardly extended to many particles and the main above properties are retained. Possible applications to the Bose-Einstein condensation with dipole-dipole interactions are briefly discussed.

New references added, implications with Bose-Einstein condensationare discussed and some portions of the manuscript rewritten

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• Dynamics of a Dirac Fermion in the presence of spin noncommutativity
• An Introduction to Noncommutative Physics
• Dynamical noncommutativity
• Noncommutative spaces and matrix embeddings on flat R^{2n+1}
• Rotationally invariant noncommutative phase space of canonical type with recovered weak equivalence principle
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• Classical electrodynamics in a space with spin noncommutativity of coordinates
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• Time reversal and rotational symmetries in noncommutative phase space
• Noncommutative Complex Scalar Field and Casimir Effect
• Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach
• Microcausality of spin-induced noncommutative theories
• Minimal momentum estimation in noncommutative phase space of canonical type with preserved rotational and time reversal symmetries
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• Dynamics determines geometry
• Chiral Spin Noncommutative Space and Anomalous Dipole Moments
• Vacuum Pair Creation in Spin Noncommutative of Coordinates: Volkov Background and Constant Electric Field