Institute of Theoretical Physics,

National Science Center ''Kharkov Institute of Physics and Technology",

Kharkov, UKRAINE

E-mail: v_tsuk@ic.kharkov.ua

**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.