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

Selected Publications of Raimar Wulkenhaar

$\bullet$ H. Grosse, A. Sako, and R. Wulkenhaar. {Exact solution of matricial $\Phi^3_2$ quantum field theory}. Nucl.\ Phys.\ B, 925:319–347, 2017.

$\bullet$ H. Grosse and R. Wulkenhaar. {On the fixed point equation of a solvable 4D QFT model}. Vietnam J. Math., 44:153–180, 2016.

$\bullet$ H. Grosse and R. Wulkenhaar. {Self-dual noncommutative $\phi^4$-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory}. Commun. Math. Phys., 329:1069–1130, 2014.

$\bullet$ V. Gayral and R. Wulkenhaar. {Spectral geometry of the Moyal plane with harmonic propagation}. J. Noncommut. Geom., 7:939–979, 2013.

$\bullet$ A. de Goursac, J.-C. Wallet, and R. Wulkenhaar. {Noncommutative induced gauge theory}. Eur. Phys. J., C51:977–987, 2007.

$\bullet$ V. Rivasseau, F. Vignes-Tourneret, and R. Wulkenhaar. {Renormalisation of noncommutative $\phi^4$-theory by multi-scale analysis}. Commun. Math. Phys., 262:565–594, 2006.

$\bullet$ H. Grosse and R. Wulkenhaar. {Renormalisation of $\phi^4$-theory on noncommutative $\mathbb R^4$ in the matrix base}. Commun. Math. Phys., 256:305–374, 2005.

$\bullet$ H. Grosse and R. Wulkenhaar. {Power-counting theorem for non-local matrix models and renormalisation}. Commun. Math. Phys., 254:91–127, 2005.

$\bullet$ H. Grosse and R. Wulkenhaar. {The $\beta$-function in duality-covariant noncommutative $\phi^4$-theory}. Eur. Phys. J., C35:277–282, 2004.

$\bullet$ T. Krajewski and R. Wulkenhaar. {Perturbative quantum gauge fields on the noncommutative torus}. Int. J. Mod. Phys., A15:1011–1030, 2000.

Current Publications

$\bullet $ H. Grosse, A. Hock, and R. 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 $ G. Münster and R. Wulkenhaar. The Leutwyler–smilga relation on the lattice. Modern Physics Letters A, 35:1950346, January 2020. doi:10.1142/s0217732319503462.

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

$\bullet $ E. Panzer and R. Wulkenhaar. Lambert-W solves the noncommutative $\Phi ^4$-model. Communications in Mathematical Physics, October 2019. doi:10.1007/s00220-019-03592-4.

$\bullet $ J. de Jong and R. 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. URL:, arXiv:1809.09453, doi:10.1063/1.5063293.

$\bullet $ H. Grosse, A. Hock, and R. Wulkenhaar. Solution of the self-dual $\Phi ^4$ QFT-model on four-dimensional Moyal space. arXiv e-prints, August 2019. URL:, arXiv:1908.04543.

$\bullet $ R. Pascalie, C. I. Pérez-Sánchez, A. Tanasa, and R. 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. URL:, doi:10.1063/1.5080306.

$\bullet $ H. Grosse, A. Hock, and R. Wulkenhaar. Solution of all quartic matrix models. arXiv e-prints, June 2019. URL:, arXiv:1906.04600.

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

$\bullet $ H. Grosse, A. Hock, and R. Wulkenhaar. A Laplacian to compute intersection numbers on $\overline \mathcal M _g,n$ and correlation functions in NCQFT. arXiv e-prints, March 2019. URL:, arXiv:1903.12526.

$\bullet $ R. 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. Springer International Publishing, 2019. URL:, doi:10.1007/978-3-030-29597-4_11.

$\bullet $ R. Pascalie, C. I. Pérez-Sánchez, and R. Wulkenhaar. Correlation functions of $\mathrm U(N)$-tensor models and their Schwinger-Dyson equations. arXiv e-prints, June 2017. URL:, arXiv:1706.07358.