Translation-Invariant Noncommutative Renormalization
arXiv:1003.4877 · doi:10.3842/SIGMA.2010.047
Abstract
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.
v2: insights on the renormalizability proof and on the commutative limit of the model were added, typos corrected, some references added, accepted for publication in the SIGMA Special Issue "Noncommutative Spaces and Fields" (Edited by P. Aschieri, H. Grosse, G. Landi and R. Szabo); v3: published version
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