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 qq¯ case we find the same semirelativistic potential obtained in preceding papers but for a question of ordering. In the 3q case we find a spin-dependent potential identical to that already derived in the literature from the ad hoc and incorrect assumption of scalar confinement. Furthermore we obtain the correct form of the spin-independent potential up to the 1/m² order.