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Noncommutative quantum field theory

Autor(en)
Harald Grosse, Raimar Wulkenhaar
Abstrakt

We summarize our recent construction of the phi(4)-model on four-dimensional Moyal space. This is achieved by solving the quartic matrix model for a general external matrix in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of that matrix. The beta-function vanishes identically. For the Moyal model, the theory of Carleman type singular integral equations reduces the construction to a fixed point problem. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. The Schwinger 2-point function is reflection positive iff the diagonal matrix 2-point function is a Stieltjes function.

Organisation(en)
Mathematische Physik
Externe Organisation(en)
Universität Münster
Journal
Fortschritte der Physik
Band
62
Seiten
797-811
Anzahl der Seiten
15
ISSN
0015-8208
DOI
https://doi.org/10.1002/prop.201400020
Publikationsdatum
09-2014
Peer-reviewed
Ja
ÖFOS 2012
103019 Mathematische Physik
Schlagwörter
ASJC Scopus Sachgebiete
Allgemeine Physik und Astronomie
Link zum Portal
https://ucrisportal.univie.ac.at/de/publications/44f02ee0-f9f4-4621-9113-80c95ea56112