Lambert-W Solves the Noncommutative Phi(4)-Model

摘要

The closed Dyson-Schwinger equation for the 2-point function of the non-commutative lambda phi(4)(2)-model is rearranged into the boundary value problem for a sectionally holomorphic function in two variables. We prove an exact formula for a solution in terms of Lambert's W-function. This solution is holomorphic in. inside a domain which contains (-1/log 4,infinity). Our methods include the Hilbert transform, perturbation series and Lagrange-Burmann resummation.