Nonrelativistic Particle in Free Random Gauge Background

TL;DR

This paper analyzes the spectral properties of a nonrelativistic particle with internal color degrees of freedom in a free random gauge background, revealing differences in energy distribution near zero momentum depending on the particle's spin.

Contribution

It applies the concept of freeness from free probability theory to solve the spectrum of a colored particle in a random gauge background analytically.

Findings

Spinless particle energy distribution exhibits a gap near zero momentum.

Particle with spin has no gap in energy distribution near zero momentum.

Spectrum can be analytically derived in the large-N limit.

Abstract

The problem of a nonrelativistic particle with an internal color degree of freedom, with and without spin, moving in a free random gauge background is discussed. Freeness is a concept developed recently in the mathematical literature connected with noncommuting random variables. In the context of large-N hermitian matrices, it means that the the multi-matrix model considered contains no bias with respect to the relative orientations of the matrices. In such a gauge background, the spectrum of a colored particle can be solved for analytically. In three dimensions, near zero momentum, the energy distribution for the spinless particle displays a gap, while the energy distribution for the particle with spin does not.