Renormalizable noncommutative quantum field theory

Autor(en)

Harald Grosse, Raimar Wulkenhaar

Abstrakt

We discuss the Euclidean noncommutative phi(4)(4)-quantum field theory as an example of a renormalizable field theory. Using a Ward identity, Disertori, Gurau, Magnen and Rivasseau were able to prove the vanishing of the beta function for the coupling constant to all orders in perturbation theory. We extend this work and obtain from the Schwinger-Dyson equation a non-linear integral equation for the renormalised two-point function alone. The non-trivial renormalised four-point function fulfils a linear integral equation with the inhomogeneity determined by the two-point function. These integral equations might be the starting point of a nonperturbative construction of a Euclidean quantum field theory on a noncommutative space. We expect to learn about renormalisation from this almost solvable model.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Universität Münster

Journal

General Relativity and Gravitation

Band

43

Seiten

2491-2498

Anzahl der Seiten

8

ISSN

0001-7701

DOI

https://doi.org/10.1007/s10714-010-1065-6

Publikationsdatum

2011

Peer-reviewed

Ja

ÖFOS 2012

103004 Astrophysik, 103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/59984818-b43e-4edb-9a99-d2d1013c3775