A Two-Loop Test of M(atrix) Theory

We consider the scattering of two Dirichlet zero-branes in M(atrix) theory. Using the formulation of M(atrix) theory in terms of ten-dimensional super Yang-Mills theory dimensionally reduced to (0 + 1)-dimensions, we obtain the effective (velocity dependent) potential describing these particles. At one-loop we obtain the well known result for the leading order of the effective potential Veff ∼ v/r, where v and r are the relative velocity and distance between the two zero-branes respectively. A calculation of the effective potential at two-loops shows that no renormalizations of the v-term of the effective potential occur at this order.