Connection between the symmetry properties of the Dirac and Maxwell equations. Conservation laws. (English. Russian original) Zbl 1189.78007
Theor. Math. Phys. 87, No. 1, 386-393 (1991); translation from Teor. Mat. Fiz. 87, No. 1, 76-85 (1991).
Summary: 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.
MSC:
| 78A25 | Electromagnetic theory (general) |
| 81V45 | Atomic physics |
| 78A02 | Foundations in optics and electromagnetic theory |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
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