{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:35:48Z","timestamp":1760236548089,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,1]],"date-time":"2021-12-01T00:00:00Z","timestamp":1638316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein\u2013Gordon equation (KGE). We demonstrate that all the solutions to the DE (possessing point- or string-like singularities) can be obtained via differentiation of a corresponding pair of the KGE solutions for a doublet of scalar fields. In this way, we obtain a \u201cspinor analogue\u201d of the mesonic Yukawa potential and previously unknown chains of solutions to DE and KGE, as well as an exceptional solution to the KGE and DE with a finite value of the field charge (\u201clocalized\u201d de Broglie wave). The pair of scalar \u201cpotentials\u201d is defined up to a gauge transformation under which corresponding solution of the DE remains invariant. Under transformations of Lorentz group, canonical spinor transformations form only a subclass of a more general class of transformations of the solutions to DE upon which the generating scalar potentials undergo transformations of internal symmetry intermixing their components. Under continuous turn by one complete revolution the transforming solutions, as a rule, return back to their initial values (\u201cspinor two-valuedness\u201d is absent). With an arbitrary solution of the DE, one can associate, apart from the standard one, a non-canonical set of conserved quantities, positive definite \u201cenergy\u201d density among them, and with any KGE solution-positive definite \u201cprobability density\u201d, etc. Finally, we discuss a generalization of the proposed procedure to the case when the external electromagnetic field is present.<\/jats:p>","DOI":"10.3390\/sym13122288","type":"journal-article","created":{"date-parts":[[2021,12,2]],"date-time":"2021-12-02T02:56:14Z","timestamp":1638413774000},"page":"2288","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["New Symmetries, Conserved Quantities and Gauge Nature of a Free Dirac Field"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8277-9139","authenticated-orcid":false,"given":"Vladimir V.","family":"Kassandrov","sequence":"first","affiliation":[{"name":"Institute of Gravitation and Cosmology, Peoples\u2019 Friendship University of Russia (RUDN University), 117198 Moscow, Russia"}]},{"given":"Nina V.","family":"Markova","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Peoples\u2019 Friendship University of Russia (RUDN Univeresity), 117198 Moscow, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,1]]},"reference":[{"key":"ref_1","unstructured":"Cartan, E. 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