caa a22 4500 445385995 CHVBK 20180317143032.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s10714-010-1065-6 doi (NATIONALLICENCE)springer-10.1007/s10714-010-1065-6 Renormalizable noncommutative quantum field theory [Elektronische Daten] [Harald Grosse, Raimar Wulkenhaar] 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. Springer Science+Business Media, LLC, 2010 Noncommutative field theory nationallicence Ward identity nationallicence Schwinger-Dyson equation nationallicence Integral equations nationallicence Grosse Harald Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090, Vienna, Austria aut Wulkenhaar Raimar Mathematisches Institut der Westfälischen Wilhelms-Universität, Einsteinstraße 62, 48149, Munster, Germany aut General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/9(2011-09-01), 2491-2498 0001-7701 43:9<2491 2011 43 10714 https://doi.org/10.1007/s10714-010-1065-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10714-010-1065-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grosse Harald Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090, Vienna, Austria aut NATIONALLICENCE 700 1- Wulkenhaar Raimar Mathematisches Institut der Westfälischen Wilhelms-Universität, Einsteinstraße 62, 48149, Munster, Germany aut NATIONALLICENCE 773 0- General Relativity and Gravitation Springer US; http://www.springer-ny.com 43/9(2011-09-01), 2491-2498 0001-7701 43:9<2491 2011 43 10714 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer