The nonlinear group representation method in the nonlinear spinor theory

Nonlinear spinor equations are derived in the paper by the nonlinear symmetry-group representation method. The basic field transforms according to the linear spinor representation of the orthochronous Lorentz group Lt. The internal symmetry group G^r is realized as a group of nonlinear transformations of the field . The invariant nonlinear spinor equations constituting the group G^r are found in terms of the covariant derivative. The group SU(2) is considered as an example.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 49–55, December, 1972.The author thanks D. D. Ivanenko and D. F. Kurdgelaidze for stimulating discussions and support.