Research Interests
$\bullet$ Non-perturbative construction of matricial quantum field theories.
$\bullet$ Quantum field theory on noncommutative geometries.
$\bullet$ Spectral noncommutative geometry.
$\bullet$ Tensorial group field theory.
$\bullet$ Renormalisation group.
• Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar Solution of all quartic matrix models. Advances in Mathematics Vol. 481, 2025 online
• Schürmann, Jörg; Wulkenhaar, Raimar An algebraic approach to a quartic analogue of the Kontsevich model. Mathematical Proceedings Vol. 174 (3), 2023 online
• Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar A Laplacian to compute intersection numbers on M_{g,n} and correlation functions in NCQFT. Communications in Mathematical Physics Vol. 399, 2023 online
• Branahl, Johannes; Hock, Alexander; Wulkenhaar, Raimar Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures. Communications in Mathematical Physics Vol. 393, 2022 online
• Wulkenhaar, Raimar Quantum field theory on noncommutative spaces. Advances in Noncommutative Geometry, 2019, pp 607-690 online
• Panzer, Erik; Wulkenhaar, Raimar Lambert-W solves the noncommutative ϕ4-model. Communications in Mathematical Physics Vol. 374, 2020, pp 1935-1961 online
• Grosse, Harald; Wulkenhaar, Raimar Self-dual noncommutative ϕ4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory. to appear in Commun. Math. Phys.Communications in Mathematical Physics Vol. 329 (3), 2014 online
• Rivasseau, Vincent; Vignes-Tourneret, Fabien; Wulkenhaar, Raimar Renormalisation of noncommutative ϕ4-theory by multi-scale analysis. Communications in Mathematical Physics Vol. 262 (3), 2006, pp 565-594 online
• Grosse, Harald; Wulkenhaar, Raimar Renormalisation of ϕ4-Theory on Noncommutative ℝ4 in the Matrix Base. Communications in Mathematical Physics Vol. 256 (2), 2005, pp 305-374 online
• Grosse, Harald; Wulkenhaar, Raimar Power-counting theorem for non-local matrix models and renormalisation. Communications in Mathematical Physics Vol. 254 (1), 2005, pp 91-127 online
Recent Publications of Prof. Dr. Raimar Wulkenhaar
$\bullet $ Alexander Hock, Sergey Shadrin, and Raimar Wulkenhaar. Symmetry of meromorphic differentials produced by involution identity and relation to integer partitions. Annales de l’Institut Henri Poincaré D, Combinatorics, Physics and their Interactions, March 2026. doi:10.4171/aihpd/231.
$\bullet $ Fridolin Melong and Raimar Wulkenhaar. Generalized super-$W_{1+\infty }$-$n$-algebra and Landau problem. Journal of Mathematical Physics, February 2026. doi:10.1063/5.0280439.
$\bullet $ Harald Grosse, Naoyuki Kanomata, Akifumi Sako, and Raimar Wulkenhaar. Relationship between a $\Phi ^4$ matrix model and harmonic oscillator systems. Letters in Mathematical Physics, February 2026. doi:10.1007/s11005-026-02049-9.
$\bullet $ Raimar Wulkenhaar. Linear relations supplementing BKP for the Kontsevich matrix model with even potential. arXiv e-prints, August 2025. arXiv:2508.04245.
$\bullet $ Alexander Hock and Raimar Wulkenhaar. Blobbed topological recursion from extended loop equations. Journal of Geometry and Physics, 212:105457, June 2025. doi:10.1016/j.geomphys.2025.105457.
$\bullet $ Fridolin Melong and Raimar Wulkenhaar. Characterization of the $W_{1+\infty }$-n-algebra and applications. arXiv e-prints, April 2025. arXiv:2504.12994.
$\bullet $ Chunqiu Song, Hendrik Weber, and Raimar Wulkenhaar. Stochastic quantization of $\lambda \phi _2^4$- theory in 2-d Moyal space. arXiv e-prints, February 2025. arXiv:2502.02355.
$\bullet $ H. Grosse, N. Kanomata, A. Sako, and R. Wulkenhaar. Relationship between $\Phi ^4$-matrix model and N-body harmonic oscillator or Calogero-Moser model. Journal of Physics: Conference Series, 2912(1):012014, December 2024. doi:10.1088/1742-6596/2912/1/012014.
$\bullet $ Alexander Hock and Raimar Wulkenhaar. Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 (with an appendix by Maciej Dołęga). Ann. Inst. Henri Poincaré Comb. Phys. Interact., July 2024. doi:10.4171/AIHPD/198.
$\bullet $ Gaëtan Borot and Raimar Wulkenhaar. A note on BKP for the Kontsevich matrix model with arbitrary potential. Symmetry, Integrability and Geometry: Methods and Applications, June 2024. doi:10.3842/sigma.2024.050.
$\bullet $ Harald Grosse, Naoyuki Kanomata, Akifumi Sako, and Raimar Wulkenhaar. Real symmetric $\Phi ^4$-matrix model as Calogero–Moser model. Letters in Mathematical Physics, February 2024. doi:10.1007/s11005-024-01772-5.
$\bullet $ Harald Grosse, Naoyuki Kanomata, Akifumi Sako, and Raimar Wulkenhaar. Real symmetric $\Phi ^4$-matrix model as Calogero-Moser model. arXiv e-prints, November 2023. arXiv:2311.10974.
$\bullet $ Fridolin Melong and Raimar Wulkenhaar. Generalized Heisenberg–Virasoro algebra and matrix models from quantum algebra. Journal of Mathematical Physics, 64(7):073505, July 2023. doi:10.1063/5.0150975.
$\bullet $ Gaëtan Borot and Raimar Wulkenhaar. A short note on BKP for the Kontsevich matrix model with arbitrary potential. arXiv e-prints, June 2023. arXiv:2306.01501.
$\bullet $ Jörg Schürmann and Raimar Wulkenhaar. An algebraic approach to a quartic analogue of the Kontsevich model. Mathematical Proceedings of the Cambridge Philosophical Society, 174(3):471–495, May 2023. doi:10.1017/S0305004122000366.
$\bullet $ Alexander Hock, Harald Grosse, and Raimar Wulkenhaar. A Laplacian to compute intersection numbers on $\bar {\mathcal {M}}_{g,n}$ and correlation functions in NCQFT. Comm. Math. Phys., 399(1):481–517, April 2023. doi:10.1007/s00220-022-04557-w.
$\bullet $ Finn Bjarne Kohl and Raimar Wulkenhaar. Intersection theory of the complex quartic Kontsevich model. arXiv e-prints, December 2022. arXiv:2212.01359.
$\bullet $ Johannes Branahl, Alexander Hock, Harald Grosse, and Raimar Wulkenhaar. From scalar fields on quantum spaces to blobbed topological recursion. J. Phys. A: Math. Theor., 55(42):423001, October 2022. doi:10.1088/1751-8121/ac9260.
$\bullet $ Johannes Branahl, Alexander Hock, and Raimar Wulkenhaar. Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures. Commun. Math. Phys., 393(3):1529–1582, August 2022. doi:10.1007/s00220-022-04392-z.
$\bullet $ Jins de Jong, Alexander Hock, and Raimar Wulkenhaar. Nested Catalan tables and a recurrence relation in noncommutative quantum field theory. Ann. Inst. Henri Poincaré D, 9(1):47–72, April 2022. doi:10.4171/aihpd/113.
$\bullet $ Johannes Branahl, Alexander Hock, and Raimar Wulkenhaar. Perturbative and geometric analysis of the quartic Kontsevich model. SIGMA Symmetry Integrability Geom. Methods Appl., 17:Paper No. 085, 33, September 2021. doi:10.3842/SIGMA.2021.085.
$\bullet $ Romain Pascalie, Carlos I. Pérez-Sánchez, and Raimar Wulkenhaar. Correlation functions of $U(N)$-tensor models and their Schwinger–Dyson equations. Ann. Inst. Henri Poincaré D, 8(3):377–458, September 2021. doi:10.4171/aihpd/107.
$\bullet $ Johannes Branahl, Alexander Hock, and Raimar Wulkenhaar. Perturbative and geometric analysis of the quartic Kontsevich model. arXiv e-prints, December 2020. arXiv:2012.02622.
$\bullet $ Erik Panzer and Raimar Wulkenhaar. Lambert-W solves the noncommutative $\Phi ^4$-model. Commun. Math. Phys., 374:1935–1961, March 2020. doi:10.1007/s00220-019-03592-4.
$\bullet $ Harald Grosse, Alexander Hock, and Raimar Wulkenhaar. Solution of the self-dual $\Phi ^4$ QFT-model on four-dimensional Moyal space. J. High Energy Phys., 01:081, January 2020. doi:10.1007/jhep01(2020)081.
$\bullet $ Gernot Münster and Raimar Wulkenhaar. The Leutwyler–Smilga relation on the lattice. Mod. Phys. Lett. A, 35:1950346, January 2020. doi:10.1142/s0217732319503462.
$\bullet $ Raimar Wulkenhaar. Quantum field theory on noncommutative spaces. In A. Chamseddine, C Consani, N Higson, M Khalkhali, H Moscovici, and G Yu, editors, Advances in Noncommutative Geometry, pages 607–690. January 2020. doi:10.1007/978-3-030-29597-4_11.
$\bullet $ Jins de Jong and Raimar Wulkenhaar. Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling. J. Math. Phys., 60(8):083504, August 2019. doi:10.1063/1.5063293.
$\bullet $ Romain Pascalie, Carlos I. Pérez-Sánchez, Adrian Tanasa, and Raimar Wulkenhaar. On the large N limit of Schwinger-Dyson equations of a rank-3 tensor field theory. J. Math. Phys., 60(7):073502, July 2019. doi:10.1063/1.5080306.
$\bullet $ Harald Grosse, Alexander Hock, and Raimar Wulkenhaar. Solution of all quartic matrix models. arXiv e-prints, June 2019. arXiv:1906.04600.
$\bullet $ Harald Grosse and Raimar Wulkenhaar. How Prof. Zeidler supported our research on exact solution of quantum field theory toy models. Vietnam J. Math., 47(1):93–112, March 2019. doi:10.1007/s10013-018-0302-2.