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.
