Abstract
We have obtained exact static plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of invariant , taking into account their own gravitational field. It is shown that the initial set of the Einstein and spinor field equations with a power-law nonlinearity have regular solutions with a localized energy density of the spinor field only if m=0 (m is the mass parameter in the spinor field equations). Equations with power and polynomial nonlinearities are studied in detail. In this case, a soliton-like configuration has negative energy. We have also obtained exact static plane-symmetric solutions to the above spinor field equations in flat space-time. It is proved that in this case soliton-like solutions are absent.
Highlights
The consideration of the nonlinear generalization of classical field theory is the only possibility to overcome the shortcomings to the theory which considers elementary particles as materials points
We obtain the soliton-like solutions which are used in the formation of the fields configurations of elementary particles with limited total energy and localized energy density
We choose the nonlinear terms in the spinor field equations which are arbitrary functions of
Summary
The consideration of the nonlinear generalization of classical field theory is the only possibility to overcome the shortcomings to the theory which considers elementary particles as materials points. In these conditions, we obtain the soliton-like solutions which are used in the formation of the fields configurations of elementary particles with limited total energy and localized energy density. Shikin have obtained exact plane-symmetric solutions to the spinor field equations with nonlinear terms which are arbitrary functions of the invariant S =ψψ , taking into account their own gravitational field They have studied in detail equations with power and polynomial nonlinearities. The aim of the paper is to study the role of nonlinear spinor as well as the own gravitational field in the formation of configurations of elementary particles with localized energy density and limited total energy In this optic, we choose the nonlinear terms in the spinor field equations which are arbitrary functions of ( ) I=P P=2 iψγ 2ψ
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