SMuK 2021 – wissenschaftliches Programm
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 13: HV 4: Quantum Field Theory in Noncommutative Spacetime
MP 13.1: Hauptvortrag
Donnerstag, 2. September 2021, 11:00–11:40, H6
Exact solution of the scalar QFT Φ4 model on the 4-dimensional noncommutative Moyal space — •Alexander Hock — Mathematisches Institut Münster, Deutschland
Local QFT, as it is used in the Standard Model, can be generalized to a non-local QFT by introducing a noncommuting ⋆-product in the action functional.
Mainly, we will focus on the scalar Φ4 Model, which breaks down at the self-dual point and for large noncommutativity to a Matrix Model. In this limit, the tower of Dyson-Schwinger equations decouple to nonlinear integral equations. We will solve these equations and show the exact solution of the planar 2-point function in 4 dimensions.
Expanding this result for small coupling constants fits perfectly with the perturbative expansion into Feynman graphs renormalized by Zimmermann’s forest formula. We emphazise that this model admits perturbatively the renormalon problem, but is nevertheless resummable.