Equivalence transformations for systems of equations of scalar and spinor fields

S. A. Vladimirov ; A. v. Konarev

Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 2, pp. 190-197

Résumé

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.