  We propose a general formulation of perturbative quantum field theory on
(finitely generated) projective modules over noncommutative algebras. This is
the analogue of scalar field theories with non-trivial topology in the
noncommutative realm. We treat in detail the case of Heisenberg modules over
noncommutative tori and show how these models can be understood as large
rectangular pxq matrix models, in the limit p/q->theta, where theta is a
possibly irrational number. We find out that the modele is highly sensitive to
the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We
give a way to cure the entanglement and prove one-loop renormalizability.
