# A semi-classical transport equation for the chiral quarks surrounding a SU(2) t'Hooft-Polyakov monopole

## TL;DR

This paper derives a semi-classical transport equation for chiral quarks near an SU(2) monopole, revealing complex current flows and distinct quasi-particle states with different dispersion relations.

## Contribution

It introduces a novel semi-classical transport framework for chiral quarks in monopole fields, detailing the properties of two quasi-particle states and their equilibrium current behaviors.

## Key findings

- Red and blue currents flow oppositely transversely.
- Red and blue axial currents flow oppositely radially.
- Identification of quasi-particle states with distinct masses.

## Abstract

A transport equation of the representative quasi-particles is derived, by solving Dirac (or Dyson) equations under the semi-classical approximation, for describing the entangled motions of the red and blue chiral quarks in the vicinity of a SU(2) t'Hooft-Polyakov monopole. The representative quasi-particles have two states characterized by different dispersion relations. A ground state quasi-particle has a zero pole mass, a zero longitudinal inertial mass and a finite transverse inertial mass, while an excited quasi-particle has a finite pole mass and finite inertial masses. At equilibrium, the red and blue currents flow against each other in the transverse direction, and the red and blue axial currents flow against each other in the radial direction.