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Mathematical paradoxes of Dirac equation representations

† 
Russian Federal Nuclear Center - All-Russian Research Institute of Experimental Physics, prosp. Mira 37, Sarov, Nizhny Novgorod region, 607188, Russian Federation

This paper examines the Foldy—Wouthuysen and Feynman—Gell-Mann representations of the Dirac equation. The analysis is conducted for electrons and positrons interacting with electromagnetic fields. Versions of quantum electrodynamics are considered both within the scope of perturbation theory and in the nonperturbative case with strong electromagnetic fields. Mathematical artifacts that contradict the physical premises of the theory are identified in the studied representations of the Dirac equation. These mathematical paradoxes are resolved if the theory only employs amplitude states (real and virtual) with positive energies.

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Fulltext is also available at DOI: 10.3367/UFNe.2025.11.040057
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Keywords: Dirac equation representations, quantum electrodynamics, fermion vacuum, positive and negative energy states, mathematical paradoxes of the theory
PACS: 03.65.Pm, 11.10.St, 12.20.−m (all)
DOI: 10.3367/UFNe.2025.11.040057
URL: https://ufn.ru/en/articles/2025/12/h/
001649345300003
2-s2.0-105029082966
2025PhyU...68.1283N
Citation: Neznamov V P "Mathematical paradoxes of Dirac equation representations" Phys. Usp. 68 1283–1288 (2025)
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Received: 2nd, June 2025, revised: 6th, November 2025, 11th, November 2025

Оригинал: Незнамов В П «Математические парадоксы представлений уравнения Дирака» УФН 195 1356–1361 (2025); DOI: 10.3367/UFNr.2025.11.040057

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