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 TMF, 1991, Volume 87, Number 1, Pages 76–85 (Mi tmf5471)

Connection between the symmetry properties of the Dirac and Maxwell equations. Conservation laws

V. M. Simulik

Abstract: A family of local eight-parameter transformations that carry the massless Dirac equation into Maxwell's equations, and also connect the symmetry properties of these equations is found. It is shown that such transformations also relate the conserved quantities for the spinor and electromagnetic fields. On the basis of these connections, a new method is proposed for investigating the symmetry properties of Maxwell's equations together with a convenient method for finding the conserved quantities for the electromagnetic field. The symmetry properties of Maxwell's equations are derived from the symmetries of the massless Dirac equation, and the conservation laws for the electromagnetic field are obtained from those for the Dirac equation by replacing the spinor $\psi$ by a definite combination of components of the electromagnetic field strengths and passage to the limit $m\to 0$. A 128-dimensional invariance algebra of the free Maxwell equations in Dirac-like form is established, and 64 electromagnetic conservation laws are obtained.

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English version:
Theoretical and Mathematical Physics, 1991, 87:1, 386–393

Bibliographic databases:

Citation: V. M. Simulik, “Connection between the symmetry properties of the Dirac and Maxwell equations. Conservation laws”, TMF, 87:1 (1991), 76–85; Theoret. and Math. Phys., 87:1 (1991), 386–393

Citation in format AMSBIB
\Bibitem{Sim91} \by V.~M.~Simulik \paper Connection between the symmetry properties of the Dirac and Maxwell equations. Conservation laws \jour TMF \yr 1991 \vol 87 \issue 1 \pages 76--85 \mathnet{http://mi.mathnet.ru/tmf5471} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1122780} \zmath{https://zbmath.org/?q=an:1189.78007} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 87 \issue 1 \pages 386--393 \crossref{https://doi.org/10.1007/BF01016578} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991HG83500008} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. Yu. Krivsky, V. M. Simulik, “Dirac equation and spin 1 representations, a connection with symmetries of the Maxwell equations”, Theoret. and Math. Phys., 90:3 (1992), 265–276
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