Stability of Yang-Mills fields system in the homogeneous (anti-)self-dual background field

TL;DR

This paper investigates the stability and transition to chaos of Yang-Mills fields in a homogeneous (anti-)self-dual background using dynamical systems methods, identifying conditions for regular and chaotic behavior.

Contribution

It introduces a detailed analysis of the energy-dependent stability of Yang-Mills fields in a specific background, applying Toda criterion, Poincare sections, and Lyapunov exponents.

Findings

Existence of regular motion at low energy densities.

Critical energy density for order-chaos transition identified.

Stability depends on model parameters.

Abstract

Stability of Yang-Mills fields system in the background field is investigated basing on Toda criterion, Poincare sections and the values of the maximal Lyapunov exponents. The existence of the region of regular motion at low densities of energy is demonstrated. Critical energy density of the order-chaos transition is analyzed for the different values of the model parameter.