Abstract:In this paper we propose a translation-invariant scalar model on the Moyal space. We prove that this model does not suffer from the UV/IR mixing and we establish its renormalizability to all orders in perturbation theory.

In this paper we provide a new proof that the Grosse-Wulkenhaar noncommutative scalar Φ 4 4 theory is renormalizable to all orders in perturbation theory, and extend it to more general models with covariant derivatives. Our proof relies solely on a multiscale analysis in x space. We think this proof is simpler and could be more adapted to the future study of these theories (in particular at the non-perturbative or constructive level).

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Continuous recordings of eating and drinking under ad-lib and stable conditions in the rat show that at least 70% of total water intake is taken with meals. There is a significant positive correlation between the amount of water associated with a meal and the size of that meal and this holds for different diets and enforced feeding schedules. On a protein diet the ratio of associated water to meal size is higher than on a carbohydrate diet. During the transition from carbohydrate to protein, water intake increases but extra drinking is not at first synchronized with feeding, and the correlation between associated water and meal size is temporarily lost. After a few days, however, the rat once again synchronizes the extra water with meals and reestablishes a significant correlation. Therefore, when conditions are stable, food is an immediate stimulus of drinking and acts at a peripheral level through oropharyngeal, or possibly gastric, mechanisms. The rat seems thereby enabled to anticipate its future requirements of water before the need actually arises.Copyright () by the American Psychological Association, Inc.

Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with a 'ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, in a self-contained way, the modern tools of constructive field theory: we construct the Borel sum of the BFL perturbative series via a convergent 'cactus' expansion, and establish the 'ultraviolet' scaling of its Borel radius. Our method shows how the 'sum over triangulations' in quantum gravity can be tamed rigorously, and paves the way for the renormalization program in group field theory.

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We introduce a linearized version of group field theory. It can be viewed either as a group field theory over the additive group of a vector space or as an asymptotic expansion of any group field theory around the unit group element. We prove exact power counting theorems for any graph of such models. For linearized colored models the power counting of any amplitude is further computed in term of the homology of the graph. An exact power counting theorem is also established for a particular class of graphs of the nonlinearized models, which satisfy a planarity condition. Examples and connections with previous results are discussed.Pacs numbers: 04.60.-m, 04.60.Pp

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