Symmetry groups of field equations for spin 1/2
Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 360-372
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Methods for constructing the largest (in the S. Lie's sense) continuous symmetry
groups of partial differential equations are developed. The equations and the transformations
of the symmetry group are not supposed to be linear. The basic conception is
that of the group of a differential operator $G_D$. Some important properties of this group
are studied and used. For the fields with the spin 1/2 the group $G_D$ is constructed in an
explicite form. With the aid of the formulas obtained, the maximal group of symmetry
for an arbitrary system of free neutrinos is established. The general form of the conformal
invariant interaction is also established and group classification of the Dirac
equation with self-interactions is carried out.
@article{TMF_1977_32_3_a6,
author = {S. A. Vladimirov},
title = {Symmetry groups of field equations for spin 1/2},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {360--372},
publisher = {mathdoc},
volume = {32},
number = {3},
year = {1977},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a6/}
}
S. A. Vladimirov. Symmetry groups of field equations for spin 1/2. Teoretičeskaâ i matematičeskaâ fizika, Tome 32 (1977) no. 3, pp. 360-372. http://geodesic.mathdoc.fr/item/TMF_1977_32_3_a6/