- Home »
- Towards construction of a Wightman QFT in four dimensions

Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.

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 $\lambda\in[-0.39,0]$.

©2012 Perimeter Institute for Theoretical Physics