Abstract
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.
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