PIRSA:14080037

Towards construction of a Wightman QFT in four dimensions

Wulkenhaar, R. (2014). Towards construction of a Wightman QFT in four dimensions. Perimeter Institute. https://pirsa.org/14080037

Wulkenhaar, Raimar. Towards construction of a Wightman QFT in four dimensions. Perimeter Institute, Aug. 19, 2014, https://pirsa.org/14080037 

          @misc{ pirsa_PIRSA:14080037,
            doi = {10.48660/14080037},
            url = {https://pirsa.org/14080037},
            author = {Wulkenhaar, Raimar},
            keywords = {},
            language = {en},
            title = {Towards construction of a Wightman QFT in four dimensions},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {aug},
            note = {PIRSA:14080037 see, \url{https://pirsa.org}}
          }

Raimar Wulkenhaar Westfälische Wilhelms-Universität Münster

DOI 10.48660/14080037
Collection
Talk Type Scientific Series

Abstract

We prove that the $\lambda\phi^4_4$ quantum field theory on noncommutative Moyal space is, in the limit of infinite noncommutativity, exactly solvable in terms of the solution of a non-linear integral equation. The proof involves matrix model techniques which might be relevant for 2D quantum gravity and its generalisation to coloured tensor models of rank $\geq 3$. Surprisingly, our limit describes Schwinger functions of a Euclidean quantum field theory on standard $\mathbb{R}^4$ which satisfy the easy Osterwalder-Schrader axioms boundedness, covariance and symmetry. We prove that the decisive reflection positivity axiom is, for the 2-point function, equivalent to the question whether or not the solution of the integral equation is a Stieltjes function. The numerical solution of the integral equation leaves no doubt that this is true for coupling constants $\lambda\in[-0.39,0]$.