No confinement without Coulomb confinement

Details No confinement without Coulomb confinement No confinement without Coulomb confinement

2002-09-10

arxiv.org/abs/hep-lat/0209105v1

Phys.Rev.Lett.90:102001,2003

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages

Scientific paper

10.1103/PhysRevLett.90.102001

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 $V_{\rm coul}(R)$ which is the instantaneous part of the 44-component of the gluon propagator in Coulomb gauge, $D_{44}(\vx,t) = V_{\rm coul}(|\vx|) \delta(t)$ + (non-instantaneous). We show that if $V_D(R)$ is confining, $\lim_{R \to \infty}V_D(R) = + \infty$, then the inequality $V_D(R) \leq - C_D V_{\rm coul}(R)$ holds asymptotically at large $R$, where $C_D > 0$ is the Casimir in the representation $D$. This implies that $ - V_{\rm coul}(R)$ is also confining.

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