  We consider quantum mechanical gauge theories with sixteen supersymmetries.
The Hamiltonians or Lagrangians characterizing these theories can contain
higher derivative terms. In the operator approach, we show that the free theory
is essentially the unique abelian theory with up to four derivatives in the
following sense: any small deformation of the free theory, which preserves the
supersymmetries, can be gauged away by a unitary conjugation. We also present a
method for deriving constraints on terms appearing in an effective Lagrangian.
We apply this method to the effective Lagrangian describing the dynamics of two
well-separated clusters of D0-branes. As a result, we prove a
non-renormalization theorem for the $v^4$ interaction.
