Topological interpretation of quantum numbers

The paper shows how vector topological charges for topological excitations in nonlinear σ-models on compact one-dimensional spaces T _G and G/T _G can be defined (here G is a simple compact Lie group and T _G is its maximal commutative subgroup). Explicit solutions, their energies and interactions between different topological charges have been obtained. A possibility of topological interpretation of quantum numbers of groups and particles is discussed. Zh. éksp. Teor. Fiz. 116, 1131–1147 (October 1999)