On the fixed point equation of a solvable 4D QFT model

TL;DR

This paper proves the existence of solutions for a solvable 4D quantum field theory model on noncommutative space by applying fixed point theorems to a nonlinear operator derived from the model.

Contribution

It demonstrates that the fixed point equation for the regularised 4D QFT model satisfies Schauder's theorem, completing the model's solution.

Findings

Correlation functions expressed via fixed point solutions

Existence of solutions established for the nonlinear operator

Completes the mathematical formulation of the solvable QFT model

Abstract

The regularisation of the $\lambda\phi^4_4$-model on noncommutative Moyal space gives rise to a solvable QFT model in which all correlation functions are expressed in terms of the solution of a fixed point problem. We prove that the non-linear operator for the logarithm of the original problem satisfies the assumptions of the Schauder fixed point theorem, thereby completing the solution of the QFT model.