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Renormalization of non-commutative quantum field theory


This project aims at studying the renormalization of non-commutative field theories in a systematic way. Recently H. Grosse and R. Wulkenhaar proved that one can cure the IR/UV mixing of such theories by adding a new term in the Lagrangian. For the non-com mutative phi**4 theory, this harmonic potential term makes the theory renormalizable to all orders.

An other model is renormalizable thanks to a similar procedure: the Gross-Neveu model on the Moyal plane. Nevertheless there is currently no way of computing the missing counterterm for other non-commutative spaces. The first part of the project will be devoted to the study of the space dependency of the renormalization procedure.

We will consider different quartically interacting models (as phi**4 or Gross-Neveu) on non-commutative spaces and find the appropriate counterterms. The second part will concern the regularisation properties of non-commutative spaces. The non-commutative phi**4 model exhibits bounded renormalization group flow. In contrast its commutative counterpart has unbounded flow.

The generality of such a feature will be studied. We also want to probe non-perturbative aspects of non-commutative field theories. We will use constructive techniques to define non-perturbatively such theories. Finally we want to examine the link between String theory and these new classes of non-commutative field theories.

Call for proposal

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Dr. Karl Lueger-ring 1

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