Translation-Invariant Noncommutative Renormalization

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.

Keywords

• noncommutative quantum field theory
• Moyal space
• locality
• translation-invariance