ZERO-BRANE QUANTUM-MECHANICS

We consider low energy, nonrelativistic scattering of two Dirichlet ze ro-branes as an exercise in quantum mechanics. For weak string couplin g and sufficiently small velocity, the dynamics is governed by an effe ctive U(2) gauge theory in 0 + 1 dimensions. At low energies, D-brane scattering can reliably probe distances much shorter than the string s cale. The only length scale in the quantum mechanics problem is the el even-dimensional Planck length. This provides evidence for the role of scales shorter than the string length in the weakly coupled dynamics of type IIA strings.