  In previous work we have shown that the (\theta->\infty)-limit of
\phi^4_4-quantum field theory on noncommutative Moyal space is an exactly
solvable matrix model. In this paper we translate these results to position
space. We show that the Schwinger functions are symmetric and invariant under
the full Euclidean group. The Schwinger functions only depend on matrix
correlation functions at coinciding indices per topological sector, and
clustering is violated. We prove that Osterwalder-Schrader reflection
positivity of the Schwinger two-point function is equivalent to the question
whether the diagonal matrix two-point function is a Stieltjes function.
Numerical investigations suggest that this can at best be expected for the
wrong sign of the coupling constant. The corresponding Wightman functions would
describe particles which interact without momentum transfer. The theory differs
from a free theory by the presence of non-trivial topological sectors.
