Geodesic
Equivalence transformations for systems of equations of scalar and spinor fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 2, pp. 190-197 
S. A. Vladimirov; A. v. Konarev. Equivalence transformations for systems of equations of scalar and spinor fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 2, pp. 190-197. http://geodesic.mathdoc.fr/item/TMF_1981_49_2_a4/
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     author = {S. A. Vladimirov and A. v. Konarev},
     title = {Equivalence transformations for systems of equations of scalar and spinor fields},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {190--197},
     year = {1981},
     volume = {49},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_49_2_a4/}
}
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A study is made of the system of differential equations which describes scalar and spinor fields and is represented in the form of a system $(S)$ of first order. The differential operators (the left-hand side of the system $(S)$) are given by the Weyl operator $\sigma^i\partial_i$ and the Kemmer–Duffin operator $\beta^i\partial_i$. The interaction is introduced on the right-hand side of the system $(S)$ and depends on the scalar fields, their first derivatives, and the spinor fields. The largest Lie group of transformations of the system $(S)$ which leaves the lefthand side of the system $(S)$ invariaat is constructed explicitly. On the basis of the obtained results, a generalization is given of Dyson's theorem on the equivalence of field models containing scalar couplings and derivative couplings.

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