Renormalization of a Noncommutative Field Theory

Autor(en)

Harald Grosse, Raimar Wulkenhaar

Abstrakt

We discuss a special Euclidean phi(4)(4)-quantum field theory over quantized space-time as an example of a renormalizable field theory. Using a Ward identity, it was possible 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 nonlinear integral equation for the renormalized two-point function alone. The nontrivial renormalized four-point function fulfills 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 renormalization from this almost solvable model.

Organisation(en)

Mathematische Physik

Externe Organisation(en)

Universität Münster

Journal

International Journal of Modern Physics A

Band

27

Anzahl der Seiten

10

ISSN

0217-751X

DOI

https://doi.org/10.1142/S0217751X12500674

Publikationsdatum

2012

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/82ed21dc-4c04-458a-bf97-b03e253c243c