CONFINEMENT IN THE COULOMB GAUGE-MODEL

The Coulomb gauge model of QCD is studied with the introduction of a c onfining potential into the scalar part of the Vector potential. Using a Green function formalism; we derive the self-energy for this model, which has both scalar and vector parts, Sigma(S)(p) and Sigma(V)(p). A rotation of these variables leads to the so-called gap and energy eq uations. We then analyse the divergence structure of these equations. As this depends explicitly on the form of potential, we give as exampl es both the linear plus Coulomb and quadratically confining potentials . The nature of the confining single particle Green function is invest igated, and shown to be divergent due to the infrared singularities ca used by the confining potential. Solutions to the gap equation for the simpler case of quadratic confinement are found both semi-analyticall y and numerically. At finite temperatures, the coupled set of equation s are solved numerically in two decoupling approximations. Although ch iral symmetry is found only to be exactly restored as T -->infinity, t he chiral condensate displays a steep drop over a somewhat small tempe rature range. (C) 1997 Academic Press.