Quark self-energy

Abstract

A model of colored quarks interacting through non-Abelian vector gauge potentials is analyzed. An analogy with the Kondo effect of solid-state physics is exploited to suggest approximations to the coupled integral equations for the quark field two-point function. Conditions are described for which the self-consistently determined quark mass equals infinity. A covariant bound-state equation for color singlet mesons is derived which is essentially three-dimensional. The internal Minkowski space, parametrized by the relative coordinate four-vector $x^{\mu }$, is replaced by a hyperplane in that space defined by $x^{\mu }{P}_{\mu }=0\mathrm{}$, $P^{\mu }$ being the four-momentum of the meson. Thus, "quark confinement" to the "inside" of the meson induces a contraction of the four-dimensional, internal Minkowski space to that hypersurface orthogonal to $P^{\mu }$. Some pecularities of the equation are briefly discussed.