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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.
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H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} -theory on noncommutative ℝ 4 \mathbb{R}^{4} in the matrix base,” Commun. Math. Phys. 256
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H. Grosse and R. Wulkenhaar, “Numerical investigation of an exactly solvable noncommutative quantum field theory in four dimensions,” in preparation
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