Research Interests

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.

Selected Publications

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
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
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
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
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
Wulkenhaar, Raimar Quantum field theory on noncommutative spaces. Advances in Noncommutative Geometry, 2019, pp 607-690 online
Schürmann, Jörg; Wulkenhaar, Raimar An algebraic approach to a quartic analogue of the Kontsevich model. Mathematical Proceedings Vol. 2022, 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
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

Current Publications

Current Publications

$\bullet$ 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.

$\bullet$ Johannes Branahl, Alexander Hock, and Raimar Wulkenhaar. Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures. arXiv e-prints, August 2020. arXiv:2008.12201.

$\bullet$ Erik Panzer and Raimar Wulkenhaar. Lambert-W solves the noncommutative $\Phi ^4$-model. Communications in Mathematical Physics, 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. Journal of High Energy Physics, 01:081, January 2020. doi:10.1007/jhep01(2020)081.

$\bullet$ Gernot Münster and Raimar Wulkenhaar. The Leutwyler–Smilga relation on the lattice. Modern Physics Letters A, 35:1950346, January 2020. doi:10.1142/s0217732319503462.

$\bullet$ 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.

$\bullet$ Jörg Schürmann and Raimar Wulkenhaar. Towards integrability of the quartic analogue of the Kontsevich model. arXiv e-prints, December 2019. arXiv:1912.03979.

$\bullet$ 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.

$\bullet$ Jins de Jong, Alexander Hock, and Raimar Wulkenhaar. Catalan tables and a recursion relation in noncommutative quantum field theory. arXiv e-prints, April 2019. arXiv:1904.11231.

$\bullet$ Harald Grosse, Alexander Hock, and Raimar Wulkenhaar. A Laplacian to compute intersection numbers on M_g,n and correlation functions in NCQFT. arXiv e-prints, March 2019. arXiv:1903.12526.

$\bullet$ 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.