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arXiv:2508.11015 · International Journal of Modern Physics A

The Foldy–Wouthuysen transformation with Dirac matrices in the chiral representation: closed expressions for energy operators of fermions moving in electrostatic fields

В. П. Незнамов

Published Mar 14, 2025• 2 citations
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Abstract

In this paper, we obtain the closed expressions for energy operators in the Foldy–Wouthuysen representation in the presence of electrostatic fields. We also establish the connection between the Foldy–Wouthuysen representation and the Feynman–Gell–Mann representation.
DOI
10.1142/s0217751x25500496

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In this paper we offer an expression of the general Foldy-Wouthuysen transformation in the chiral representation of Dirac matrices interacting with fermion field. Our hypothesis is that through the multiplication of the Pauli matrix and Maxwell's chiral equations in the case of ,one obtains the Dirac's chiral equation. This is the proof of the theorem that the wave mechanics of quantum particles represent a specialized electrodynamic. En este trabajo se presenta una expresión de la transformación general de Foldy-Wouthuysen a la representación quiral de las matrices de Dirac interactuando con un campo de fermión. La hipótesis es que a través de la multiplicación de la matriz de Pauli por las ecuaciones quirales de Maxwell en el caso de , se obtiene la ecuación quiral de Dirac. Esta es la prueba del teorema de que la mecánica de ondas de partícula cuántica representa una electrodinámica especializada.
The paper describes conditions for transformation from the Dirac representation to the Foldy-Wouthuysen representation. The necessary condition is the block-diagonal transformation of Hamiltonian relative to the upper and lower components of the wave function. The sufficient condition is the wave function transformation law described by relation (6). It has been demonstrated that the unitary transformations offered by the authors of the papers [14], [15], [16], [17] do not satisfy the sufficiency condition (6) and, hence, they are not the Foldy-Wouthuysen transformations. In applications, the matrix elements of any operator in the FW representation can be calculated, according to (6), using the normalized two-component wave functions in the Dirac representation known for the given problem.