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arXiv · 1504.03453

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
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Abstract

It 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 probability of particle-antiparticle pair creation and annihilation is negligible. In the weak-field limit of static and homogeneous electromagnetic fields, by applying the method of direct perturbation theory inductively on the orders of $1/c$ in the power series, we rigorously prove 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.

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Dah-Wei Chiou, Tsung-Wei Chen. 2015-04-14. Exact correspondence between classical and Dirac-Pauli spinors in the weak-field limit of static and homogeneous electromagnetic fields. https://arxiv.org/abs/1504.03453

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