Collective motions in nucleon

Abstract:
The dynamics of soliton states in SU(2) models is investigated within the framework of the variational approach to the collective variables formalism. The moduli space approximation which is a base for investigation of such kind problems is not used in present work. Collective variables are introduced from the symmetry properties of an initial Lagrangian. The gauge condition used in the work allows to turn to zero the coherent component of a canonical field momentum. In this case the variation equations are reduced to one equation for dynamic SU(2) solitons rotating independently in usual and isotopic spaces. Generally, the shape of these solitons is determined with the account of the self-consistent collective forces reflecting the presence of non-compensated dynamic stresses in the system. In the limit of axial symmetric configurations self-consistent forces turn to zero, and the generalized matrix of spin - isospin rotations becomes degenerated. The order of the passage to the limit at which singular terms disappear is indicated in the work. The equation originating in this case describes the configurations characteristic for the states of the nucleon and delta. As a whole it is possible to specify three types of semiclassical states described by the theory. First of all it is a nucleon. The corresponding state satisfies the exact equations of motion and is stable with respect to the field fluctuations. The delta - isobar also satisfies the exact equations of motion. However, the delta - isobar state is stable only in the absence of field fluctuations. All other resonances do not satisfy the equations of motion, their shape has no axial symmetry and during evolution these states continuously radiate a pi-meson field. Using the usual scale analysis in spirit of the Derrick theorem, it is shown in the work , that by virtue of the spin - isospin rotation the stable localized states can exsist in the SU(2) sigma-model. In fact this result reanimates the SU(2) sigma-model as a potential model of the nucleons.