Zero-Brane Quantum Mechanics

We consider low energy, nonrelativistic scattering of two Dirichlet zero-branes as an exercise in quantum mechanics. For weak string coupling and sufficiently small velocity, the dynamics is governed by an effective U(2) gauge theory in 0+1 dimensions. At low energies, D-brane scattering can reliably probe distances much shorter than the string scale. The only length scale in the quantum mechanics problem is the eleven-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.