In this talk, we talk about the large N problems for the Wick renormalized linear sigma model, i.e. N-component φ4 model, in two spatial dimensions, using stochastic quantization methods and Dyson–Schwinger equations. We identify the large N limiting law of a collection of Wick renormalized O(N) invariant observables. In particular, under a suitable scaling, the quadratic observables converge in the large N limit to a mean-zero (singular) Gaussian field Q with an explicit covariance; and the observables which are renormalized powers of order 2n converge in the large N limit to suitably renormalized nth powers of Q. Furthermore, we derive the 1/N expansion for the k-point functions of the quadratic observables by employing a graph representation and carefully analysing the order of each graph from Dyson-Schwinger equations. Finally, we obtain the next order stationary dynamics.
This video was produced by the University of Münster, as part of the workshop Stochastic Analysis meets QFT – critical theory.
