On the quantum mechanics of M (atrix) theory Original Research Article

We present a studu of M (atrix) theory from a purely canonical viewpoint. In particular, we identify free particle asymptotic states of the model corresponding to the supergraviton multiplet of eleven-dimensional supergravity. These states have a natural interpretation as excitations in the directions of the matrix model potential. Furthermore, we provide the split of the matrix model Hamiltonian into a free part describing the free propagation of these particles states along with the interaction Hamiltonia describing their interactions. Elementary quantum mechanical perturbation theory then yiels an effective potential for these particles as an expansion in their inverse separation. Remarkably we find the leading velocity-independent terms of the effective potential cancel in agreement with the fact that there is no force between stationary D0-branes. The scheme we present provides a framework in which one can perturbatively compute the M (atrix) theory result for the eleven-dimemsional supergration S-matrix.