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28 March 2024
 
  » arxiv » 1504.3453

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Exact correspondence between classical and Dirac-Pauli spinors in the weak-field limit of static and homogeneous electromagnetic fields
Dah-Wei Chiou ; Tsung-Wei Chen ;
Date 14 Apr 2015
AbstractIt has long been speculated that the Dirac or, more generally, the Dirac-Pauli spinor in the Foldy-Wouthuysen (FW) representation should behave like a classical relativistic spinor in the low-energy limit when the particle-antiparticle interaction is negligible. In the weak-field limit of static and homogeneous electromagnetic fields, we rigorously prove, by applying Kutzelnigg’s method inductively on the orders of $1/c$ in the power series, that it is indeed the case: the FW transformation of the Dirac-Pauli Hamiltonian is in full agreement with the classical counterpart, which is the sum of the orbital Hamiltonian for the Lorentz force equation and the spin Hamiltonian for the Thomas-Bargmann-Michel-Telegdi equation.
Source arXiv, 1504.3453
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