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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