From Noncommutative Sphere to Nonrelativistic Spin

Abstract

Reparametrization invariant dynamics on a sphere, being parameterized by angular momentum coordinates, represents an example of noncommutative theory. It can be quantized according to Berezin-Marinov prescription, replacing the coordinates by Pauli matrices. Following the scheme, we present two semiclassical models for description of spin without use of Grassman variables. The first model implies Pauli equation upon the canonical quantization. The second model produces nonrelativistic limit of the Dirac equation implying correct value for the electron spin magnetic moment.

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Cited by in corpus (2)

• Classical gauge principle -- From field theories to classical mechanics
• To square root the Lagrangian or not: an underlying geometrical analysis on classical and relativistic mechanical models