Relativistic corrections to the algebra of position variables and spin-orbital interaction

TL;DR

This paper explores how relativistic effects influence the algebra of position variables and spin-orbital interactions, providing a classical explanation for discrepancies between different Hamiltonian formulations without relying on quantum transformations.

Contribution

It introduces a covariant formalism within the vector model of spin that explains relativistic corrections to position and spin interactions classically, bypassing traditional quantum methods.

Findings

Relativistic corrections affect the algebra of position variables.

Spin-induced non-commutativity accounts for Hamiltonian discrepancies.

Classical formalism reproduces quantum Hamiltonian differences.

Abstract

In the framework of vector model of spin, we discuss the problem of a covariant formalism \cite{Pomeranskii1998} concerning the discrepancy between relativistic and Pauli Hamiltonians. We show how the spin-induced non commutativity of a position accounts the discrepancy on the classical level, without appeal to the Dirac equation and Foldy-Wouthuysen transformation.