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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 8: HV Hock: QFT in Noncommutative Space
MP 8.1: Hauptvortrag
Mittwoch, 1. April 2020, 10:30–11:10, H-HS VII
Exact solution of the noncommutative φ44 QFT model — •Alexander Hock1, Raimar Wulkenhaar1, and Harald Grosse2 — 1WWU Münster, Germany — 2University of Vienna, Austria
A noncommutative quantum field theory is a QFT where the underlying space is equipped with an additional algebraic structure. The scalar φ4 model which is also known as Grosse-Wulkenhaar model will be presented in 4 dimensions, which has the same degrees of divergence as the ordinary φ4 model.
The set of infinitely many Ward-Takahashi identities leads to closed integral equations for the correlation functions. These equations can be solved with techniques of algebraic geometry and complex analysis. The exact solution of the 2-point function will be shown which consists of hypergeometric functions. The perturbative expansion coincides with the Feynman graph computations by using Zimmermann’s forest formula.
The remarkable property is that the theory is resummable even though the renormal problem appears and the number of Feynman graphs grows with O(n!).