On the quantum mechanics of M(atrix) theory

TL;DR

This paper analyzes M(atrix) theory using canonical methods, identifying supergraviton states, splitting the Hamiltonian into free and interaction parts, and deriving an effective potential that matches expected supergravity interactions.

Contribution

It introduces a canonical framework for M(atrix) theory, identifying asymptotic supergraviton states and deriving an effective potential through perturbation theory.

Findings

Leading velocity-independent potential terms cancel, indicating no force between stationary D0 branes.

Framework allows perturbative computation of the supergraviton S matrix in eleven dimensions.

Hamiltonian split facilitates analysis of particle interactions in M(atrix) theory.

Abstract

We present a study 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 flat 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 particle states along with the interaction Hamiltonian describing their interactions. Elementary quantum mechanical perturbation theory then yields an effective potential for these particles as an expansion in their inverse separation. Remarkably we find that 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 dimensional supergraviton S matrix.