Research area B: Spaces and Operators
Unit B3: Operator algebras & mathematical physics
Research area C: Models and Approximations
Unit C1: Evolution and asymptotics
Unit C3: Interacting particle systems and phase transitions
Further Projects
• RTG 2149: Strong and Weak Interactions - from Hadrons to Dark Matter online
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.
• 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
• Panzer, Erik; Wulkenhaar, Raimar Lambert-W solves the noncommutative \Phi^4-model. Communications in Mathematical Physics Vol. 374, 2020, pp 1935-1961 online
• Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar Solution of all quartic matrix models. , 2019 online
• Schürmann, Jörg; Wulkenhaar, Raimar An algebraic approach to a quartic analogue of the Kontsevich model. Mathematical Proceedings Vol. 174 (3), 2023 online
• Wulkenhaar, Raimar Quantum field theory on noncommutative spaces. Advances in Noncommutative Geometry, 2019, pp 607-690 online
• Grosse, Harald; Wulkenhaar, Raimar Self-dual noncommutative \phi^4-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
• Grosse H, Wulkenhaar R Renormalisation of \phi^4-theory on noncommutative R^4 in the matrix base
. Communications in Mathematical Physics Vol. 256 (2), 2005, pp 305-374 online
• Rivasseau, Vincent, Vignes-Tourneret, Fabien; Wulkenhaar, Raimar Renormalisation of noncommutative \phi^4-theory by multi-scale analysis. Communications in Mathematical Physics Vol. 262 (3), 2006, pp 565-594 online
• Krajewski T, Wulkenhaar R Perturbative quantum gauge fields on the noncommutative torus. International Journal of Modern Physics A Vol. 15 (7), 2000, pp 1011-1029 online
• Grosse H, Wulkenhaar R Power-counting theorem for non-local matrix models and renormalisation. Communications in Mathematical Physics Vol. 254 (1), 2005, pp 91-127 online
Current Cluster Publications of Prof. Dr. Raimar Wulkenhaar
$\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 $ Alexander Hock, Harald Grosse, and Raimar Wulkenhaar. A Laplacian to compute intersection numbers on $\mathcal M$ and correlation functions in NCQFT. Comm. Math. Phys., 399(1):481–517, April 2023. doi:10.1007/s00220-022-04557-w.
$\bullet $ Alexander Hock and Raimar Wulkenhaar. Blobbed topological recursion from extended loop equations. arXiv e-prints, January 2023. arXiv:2301.04068.
$\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. Journal of Physics A: Mathematical and Theoretical, 55(42):423001, October 2022. doi:10.1088/1751-8121/ac9260.
$\bullet $ Jörg Schürmann and Raimar Wulkenhaar. An algebraic approach to a quartic analogue of the Kontsevich model. Mathematical Proceedings of the Cambridge Philosophical Society, pages 1–25, September 2022. doi:10.1017/S0305004122000366.
$\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 $ Alexander Hock and Raimar Wulkenhaar. Blobbed topological recursion of the quartic Kontsevich model II: Genus=0. arXiv e-prints, March 2021. arXiv:2103.13271.
$\bullet $ Erik Panzer and Raimar Wulkenhaar. Lambert-W solves the noncommutative $\Phi ^4$-model. Communications in Mathematical Physics, 374:1935–1961, March 2020. doi:10.1007/s00220-019-03592-4.
$\bullet $ Gernot Münster and Raimar Wulkenhaar. The Leutwyler–Smilga relation on the lattice. Modern Physics Letters A, 35:1950346, January 2020. doi:10.1142/s0217732319503462.
$\bullet $ Harald Grosse, Alexander Hock, and Raimar Wulkenhaar. Solution of the self-dual $\Phi ^4$ QFT-model on four-dimensional Moyal space. Journal of High Energy Physics, 01:081, January 2020. doi:10.1007/jhep01(2020)081.
$\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. Journal of Mathematical Physics, 60(8):083504, August 2019. arXiv:1809.09453, 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. Journal of Mathematical Physics, 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.