Quark sector of Coulomb gauge Quantum Chromodynamics

The quark sector of Coulomb gauge quantum chromodynamics is considered within the functional integral approach. The quark contributions to the Dyson-Schwinger equations are derived and one-loop perturbative results for the two-point functions are presented. The problem of confinement is addressed in the heavy quark limit, by rewriting the generating functional of quantum chromodynamics in terms of a heavy quark mass expansion. By restricting to leading order in this expansion and considering only the two-point functions of the Yang-Mills sector, the rainbow-ladder approximation to the gap and Bethe-Salpeter equations is shown to be exact. Analytic nonperturbative solutions to the Bethe-Salpeter equation for quark-antiquark bound states and Faddeev equation for three-quark bound states, in the case of equal quark separations, are presented. The quark-antiquark and three-quark confining potentials are derived and a direct connection between the temporal gluon propagator and the corresponding string tensions is found. It is shown that only color singlet of quark-antiquark (meson) and qqq (baryon) states are physically allowed. Moreover, the four-point Green's functions, in both quark-antiquark and diquark channels, are explicitly derived. It is found that the corresponding poles relate to the bound state energy of the heavy quark systems, and a natural separation between physical and unphysical poles in the Green's functions emerges.