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A transport equation of the representative quasi-particles is derived, bysolving Dirac (or Dyson) equations under the semi-classical approximation, fordescribing the entangled motions of the red and blue chiral quarks in thevicinity of a SU(2) t'Hooft-Polyakov monopole. The representativequasi-particles have two states characterized by different dispersionrelations. A ground state quasi-particle has a zero pole mass, a zerolongitudinal inertial mass and a finite transverse inertial mass, while anexcited quasi-particle has a finite pole mass and finite inertial masses. Atequilibrium, the red and blue currents flow against each other in thetransverse direction, and the red and blue axial currents flow against eachother in the radial direction.

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