On topological interpretation of quantum numbers

TL;DR

This paper introduces a topological framework for understanding quantum numbers through vector topological charges in non-linear sigma-models on compact homogeneous spaces, providing explicit solutions and exploring their physical implications.

Contribution

It presents a novel topological interpretation of quantum numbers by defining vector topological charges and analyzing their solutions and interactions in sigma-models.

Findings

Explicit solutions for topological charges in specific models

Analysis of energies and interactions of topological charges

Discussion on topological interpretation of quantum numbers

Abstract

It is shown how one can define vector topological charges for topological exitations of non-linear sigma-models on compact homogeneous spaces T_G and G/T_G (where G is a simple compact Lie group and T_G is its maximal commutative subgroup). Explicit solutions for some cases, their energies and interaction of different topological charges are found. A possibility of the topological interpretation of the quantum numbers of groups and particles is discussed.