Quantum field theory on projective modules

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