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Over many years, we developed the construction of the ϕ4-model on four-dimensional Moyal space. The solution of the related matrix model \(\mathcal {Z}[E,J]=\int d{\Phi } \exp (\text {tr}(J{\Phi }- E{\Phi }^{2} -\frac {\lambda }{4} {\Phi }^{4}))\) is given in terms of the solution of a non-linear equation for the 2-point function and the eigenvalues of E. The resulting Schwinger functions in position space are symmetric and invariant under the full Euclidean group. Locality is fulfilled. The Schwinger 2-point function is reflection positive in special cases.

How Prof. Zeidler Supported Our Research on Exact Solution of Quantum Field Theory Toy Models