Giovanni Maria Prosperi

Consistent derivation of the quark-antiquark and three-quark potentials in a Wilson loop context

We give a new derivation of the quark-antiquark potential in the Wilson loop context. This makes more explicit the approximations involved and enables an immediate extension to the three-quark case. In the [ital q[bar q]] case we find the same semirelativistic potential obtained in preceding papers but for a question of ordering. In the 3[ital q] case we find a spin-dependent potential identical to that already derived in the literature from the [ital ad] [ital hoc] and incorrect assumption of scalar confinement. Furthermore we obtain the correct form of the spin-independent potential up to the 1/[ital m][sup 2] order.