Aharonov-Bohm scattering for relativistic particles in (3 + 1)-dimensional noncommutative space with spin dependence

Stechhahn, C. A.

doi:10.48550/arxiv.1905.12538

Cited by 1 publication

(1 citation statement)

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“…In this regard, we point out that spinning particles represent an exceptional example of intrinsically noncommutative and relativistic-invariant theory, with the spin-induced noncommutativity that manifests itself already at the Compton scale. The effects due to noncommutative geometry are of considerable interest in the current literature [46][47][48][49][50][51][52][53][54], and certainly deserve a detailed study in the relativistic-invariant context of spin-induced noncommutativity.…”

Section: Discussionmentioning

confidence: 99%

Covariant version of the Pauli Hamiltonian, spin-induced noncommutativity, Thomas precession, and the precession of spin

Дериглазов

Tereza

2019

Phys. Rev. D

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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 1/c 2 -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.

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