On the lagrange approach and dynamical variables for the spinor field in Foldy – Wouthuysen canonical representation

Abstract

The relativistic invariant Lagrange approach for the spinor field in Foldy – Wouthuysen representation is constructed. The analogy with classical mechanics for the system with arbitrary number degrees of freedom is used for this construction. The dynamical variables for the spinor field in this representation are found. The conservation laws in terms of quantum mechanical particle-antiparticle momentum-spin amplitudes are presented. In this way the direct physical sense of the conserved quantities is demonstrated. 12 important additional conserved quantities are obtained together with 10 well-known conservation laws for the spinor field, which are the consequences of the Poincare symmetry of the theory. The additional dynamical variables are the consequences of the fact that both orbital and spin parts of the total 4-angular momentum of the spinor field are conserved independently.