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The remarkable properties of the real scalar quartic quantum field theory on the Moyal plane in combination with its similarity to the Kontsevich model make the model's partition function an interesting object to study.
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H. Grosse and H. Steinacker, “A nontrivial solvable noncommutative ϕ 3 \phi^{3} model in 4 dimensions,” J. High Energy Phys. 2006
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M. Disertori, R. Gurau, J. Magnen, and V. Rivasseau, “Vanishing of beta function of non commutative ϕ 4 4 \phi_{4}^{4} theory to all orders,” Phys. Lett. B 649
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H. Grosse and H. Steinacker, “Renormalization of the noncommutative ϕ 3 \phi^{3} model through the kontsevich model,” Nucl. Phys. B 746
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H. Grosse and R. Wulkenhaar, “Renormalisation of ϕ 4 \phi^{4} -theory on non-commutative ℝ 4 \mathbb{R}^{4} to all orders,” Lett. Math. Phys. 71
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H. Grosse and R. Wulkenhaar, “Power-counting theorem for non-local matrix models and renormalisation,” Commun. Math. Phys. 254
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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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J. de Jong, Partition function methods for the quartic scalar quantum field theory on the Moyal plane , PhD dissertation, WWU Münster (2018)
2018
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