http://dspace.nbuv.gov.ua:80/handle/123456789/145982 Fri, 24 Apr 2026 10:38:01 GMT 2026-04-24T10:38:01Z http://dspace.nbuv.gov.ua:80/bitstream/id/434970/ http://dspace.nbuv.gov.ua:80/handle/123456789/145982 http://dspace.nbuv.gov.ua:80/handle/123456789/146455 Extended Soliton Solutions in an Effective Action for SU(2) Yang-Mills Theory Sawado, N.; Shiiki, N.; Tanaka, S. The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) σ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains an additional fourth-order term which destabilizes the soliton solution. We apply the perturbative treatment to the second derivative term in order to exclude (or reduce) the ill behavior of the original action and show that the SFN model with the second derivative term possesses soliton solutions. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/146455 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/146454 Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces Hentosh, O.Ye. We obtain via Bäcklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended by evolutions of the corresponding spectral problem eigenfunctions and adjoint eigenfunctions, as well as for the hierarchies of their additional symmetries. The relation of these hierarchies with the integrable by Lax (2|1+1)-dimensional supersymmetric Davey-Stewartson system is investigated. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/146454 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/146453 On the Effective Action of Dressed Mean Fields for N = 4 Super-Yang-Mills Theory Cvetic, G.; Kondrashuk, I.; Schmidt, I. On the basis of the general considerations such as R-operation and Slavnov-Taylor identity we show that the effective action, being understood as Legendre transform of the logarithm of the path integral, possesses particular structure in N = 4 supersymmetric Yang-Mills theory for kernels of the effective action expressed in terms of the dressed effective fields. These dressed effective fields have been introduced in our previous papers as actual variables of the effective action. The concept of dressed effective fields naturally appears in the framework of solution to Slavnov-Taylor identity. The particularity of the structure is independence of these kernels on the ultraviolet regularization scale Λ. These kernels are functions of mutual spacetime distances and of the gauge coupling. The fact that β function in this theory vanishes is used significantly. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/146453 2006-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/146452 Orbit Functions Klimyk, A.; Patera, J. In the paper, properties of orbit functions are reviewed and further developed. Orbit functions on the Euclidean space En are symmetrized exponential functions. The symmetrization is fulfilled by a Weyl group corresponding to a Coxeter-Dynkin diagram. Properties of such functions will be described. An orbit function is the contribution to an irreducible character of a compact semisimple Lie group G of rank n from one of its Weyl group orbits. It is shown that values of orbit functions are repeated on copies of the fundamental domain F of the affine Weyl group (determined by the initial Weyl group) in the entire Euclidean space En. Orbit functions are solutions of the corresponding Laplace equation in En, satisfying the Neumann condition on the boundary of F. Orbit functions determine a symmetrized Fourier transform and a transform on a finite set of points. Sun, 01 Jan 2006 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/146452 2006-01-01T00:00:00Z