Dynamics of Multiparticle Systems with non - Abelian Symmetry

TL;DR

This paper studies the evolution of many-body systems with non-Abelian symmetry, deriving conditions that ensure microscopic dynamics respect the symmetry, with explicit examples for SU(2) systems involving particles like nucleons and pions.

Contribution

It provides explicit global conditions for microscopic evolution to preserve non-Abelian symmetry constraints, exemplified with SU(2) systems.

Findings

Derived explicit global symmetry-preserving conditions

Demonstrated constraint mechanisms in SU(2) systems

Analyzed particles in fundamental and adjoint representations

Abstract

We consider the dynamics governing the evolution of a many body system constrained by an nonabelian local symmetry. We obtain explicit forms of the global macroscopic condition assuring that at the microscopic level the evolution respects the overall symmetry constraint. We demonstrate the constraint mechanisms for the case of SU(2) system comprising particles in fundamental, and adjoint representations (`nucleons' and `pions').