Translation-Invariant Noncommutative Renormalization
Adrian Tanasa
TL;DR
This paper reviews the development of a translation-invariant scalar quantum field model on Moyal space that is perturbatively renormalizable, and discusses potential extensions to group field theory for quantum gravity.
Contribution
It introduces a translation-invariant scalar model on Moyal space with proven perturbative renormalizability and explores its generalization to group field theory for quantum gravity.
Findings
The scalar model is perturbatively renormalizable on Moyal space.
General considerations on nonlocal renormalizability are discussed.
Perspectives for applying these techniques to quantum gravity are presented.
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.
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