Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 6 (2010), 047, 13 pages      arXiv:1003.4877
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Translation-Invariant Noncommutative Renormalization

Adrian Tanasa a, b
a) Centre de Physique Théorique, CNRS, UMR 7644, École Polytechnique, 91128 Palaiseau, France
b) Institutul de Fizică şi Inginerie Nucleară Horia Hulubei, P.O. Box MG-6, 077125 Măgurele, România

Received March 25, 2010, in final form May 24, 2010; Published online June 08, 2010

We review here the construction of a translation-invariant scalar model which was proved to be perturbatively renormalizable on Moyal space. Some general considerations on nonlocal renormalizability are given. Finally, we present perspectives for generalizing these quantum field theoretical techniques to group field theory, a new setting for quantum gravity.

Key words: noncommutative quantum field theory; Moyal space; locality; translation-invariance.

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