Classical quark matter in one dimension: Abelian approximation

A classical quark gas in which only the diagonal elements of the SU(3) color gluon interaction are retained is studied in one dimension. By use of functional integration techniques, the grand partition function of the system is obtained by finding the least eigenvalue of a two-dimensional Schr\"odinger equation with a periodic potential. In the high-density limit, the system exhibits free-quark behavior. In the low-density limit, the equation of state approaches that of an ideal gas of three-quark bound states. The possible existence of a phase transition is considered unlikely.