Quantum field theory on projective modules

  • V. Gayral
  • Published 2006


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 p× q matrix models, in the limit p/q → θ, where θ is a possibly irrational number. We find out that the model is highly sensitive to the number-theoretical aspect of θ and suffers from an UV/IR-mixing. We give a way to cure the entanglement and prove one-loop renormalizability.

Cite this paper

@inproceedings{Gayral2006QuantumFT, title={Quantum field theory on projective modules}, author={V. Gayral}, year={2006} }