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Teoreticheskaya i Matematicheskaya Fizika, 1991, Volume 87, Number 1, Pages 76–85
(Mi tmf5471)
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This article is cited in 19 scientific papers (total in 19 papers)
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.
Received: 17.09.1990
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
Linking options:
https://www.mathnet.ru/eng/tmf5471 https://www.mathnet.ru/eng/tmf/v87/i1/p76
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