Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin
arXiv:1910.11140 · doi:10.1103/PhysRevD.100.105009
Abstract
We show that there is a manifestly covariant version of the Pauli Hamiltonian with equations of motion quadratic on spin and field strength. Relativistic covariance inevitably leads to noncommutative positions: classical brackets of the position variables are proportional to the spin. It is the spin-induced noncommutativity that is responsible for transforming the covariant Hamiltonian into the Pauli Hamiltonian, without any appeal to the Thomas precession formula. The Pauli theory can be thought to be approximation of the covariant theory written in special variables. These observations clarify the long standing question on the discrepancy between the covariant and Pauli Hamiltonians. We also discuss the transformational properties of spin axis in the passage from laboratory to comoving and instantaneous frames, and reveal the role of Thomas spin-vector in the covariant scheme.
12 pages, references added. Matches with published version. Conclusion and references expanded according to the referee requirement
References in corpus (8)
- Muon g-2: Review of Theory and Experiment
- Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
- Relativistic corrections to the algebra of position variables and spin-orbital interaction
- Particles as Wilson lines of gravitational field
- Lagrangian for the Frenkel electron
- Spin dynamics of a millisecond pulsar orbiting closely around a massive black hole
- Generalized twist deformations of Poincare and Galilei quantum groups
- Chiral Spin Noncommutative Space and Anomalous Dipole Moments