  We describe a new regularization of quantum field theory on the
noncommutative torus by means of one-dimensional matrix models. The
construction is based on the Elliott-Evans inductive limit decomposition of the
noncommutative torus algebra. The matrix trajectories are obtained via the
expansion of fields in a basis of new noncommutative solitons described by
projections and partial isometries. The matrix quantum mechanics are compared
with the usual zero-dimensional matrix model regularizations and some
applications are sketched.
