Quantum field theory on projective modules

Details Quantum field theory on projective modules Quantum field theory on projective modules

2006-12-06

arxiv.org/abs/hep-th/0612048v1

Physics

High Energy Physics

High Energy Physics - Theory

52 pages, uses feynmf

Scientific paper

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.

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