Accurate energy spectrum for the quantum Yang-Mills mechanics with nonlinear color oscillations

TL;DR

This paper computes accurate energy spectra for quantum Yang-Mills mechanics with nonlinear color oscillations in the SU(2) gauge group, using a basis expansion method and comparing with semiclassical solutions.

Contribution

It introduces an optimized trigonometric basis expansion method to diagonalize the Yang-Mills Hamiltonian with nonlinear oscillations, providing precise energy eigenvalues and eigenfunctions.

Findings

Accurate energy eigenvalues for one and two degrees of freedom.

Comparison showing agreement with semiclassical solutions.

Demonstration of the method's effectiveness for non-Abelian gauge theories.

Abstract

Yang-Mills theory as the foundation for quantum chromodynamics is a non-Abelian gauge theory with self-interactions between vector particles. Here, we study the Yang-Mills Hamiltonian with nonlinear color oscillations in the absence of external sources corresponding to the group $SU(2)$. In the quantum domain, we diagonalize the Hamiltonian using the optimized trigonometric basis expansion method and find accurate energy eigenvalues and eigenfunctions for one and two degrees of freedom. We also compare our results with the semiclassical solutions.