Formulação covariante da teoria de Pauli e precessão de Thomas

Abstract

We show that there is a manifestly covariant version of Pauli Hamiltonian. Relativistic covariance inevitably leads to non commutative positions: classical brackets of the position variables are proportional to the spin. It is the spin-induced non commutativity 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 as 1/c2−approximation of the covariant theory written in special variables. These observations clarify the long standing question on 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; we rewrote our covariant theory in terms of new variables to clarify another long-standing problem: to obtain a Hamiltonian formulation of the equations proposed by Bargmann, Michel and Telegli, for a particle with spin in the presence of an electromagnetic field (here in the general case, arbitrary field). This work was based on the article: Danilo Machado Tereza, Alexei Deriglazov, Covariant version of Pauli Hamiltonian, spin-induced non commutativity, Thomas precession and precession of spin, Phys. Rev. D 100 (2019) 105009; arXiv:1910.11140.