No confinement without Coulomb confinement.
We compare the physical potential V(D)(R) of an external quark-antiquark pair in the representation D of SU(N), to the color-Coulomb potential V(coul)(R) which is the instantaneous part of the 44-component: of the gluon propagator in Coulomb-gauge D44(x-->,t)=V(coul)(|x-->|)delta(t)+(noninstantaneous). We show that if V(D)(R) is confining, lim(V(D)(R)=+ infinity, as is believed to hold in the absence of dynamical quarks, then the inequality V(D)(R)<or=-C(D)V(coul)(R) holds asymptotically at large R, where C(D)>0 is the Casimir in the representation D. This implies that -V(coul)(R) is also confining.
Zwanziger
Daniel
D
Physics Department, New York University, New York, New York 10003, USA.