Professor Dr. Raimar Wulkenhaar

• 2025
• 2024
• 2023
• 2022
• 2021
• 2020
• 2019
• 2018
• 2017
• 2016
• 2015
• 2014
• 2013
• 2012
• 2011
• 2010
• 2009
• 2008
• 2007
• 2006
• 2005
• 2004
• 2003
• 2002
• 2001
• 2000
• 1999
• 1998
• 1997
• 1996

2025

• Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. 2025. “Solution of all quartic matrix models.” Advances in Mathematics 481 110551. doi: 10.1016/j.aim.2025.110551.
• Wulkenhaar, Raimar. 2025. “Linear relations supplementing BKP for the Kontsevich matrix model with even potential.” Preprint. arXiv doi: 10.48550/arXiv.2508.04245.
• Grosse, Harald, Kanomata, Naoyuki, Sako, Akifumi, and Wulkenhaar, Raimar. 2025. “Relationship between a Φ^4 matrix model and harmonic oscillator systems.” Preprint. arxiv doi: 10.48550/arXiv.2507.09454.
• Melong, Fridolin, and Wulkenhaar, Raimar. 2025. “Generalized super-W_{1+∞}-n-algebra and Landau Problem.” Preprint. arXiv doi: 10.48550/arXiv.2504.13319.
• Hock, Alexander, and Wulkenhaar, Raimar. 2025. “Blobbed topological recursion from extended loop equations.” Journal of Geometry and Physics 212 105457. doi: 10.1016/j.geomphys.2025.105457.
• Hock, Alexander, Shadrin, Sergey, and Wulkenhaar, Raimar. 2025. “Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions.” Preprint. arXiv doi: 10.48550/arXiv.2501.00082.
• Song, Chunqiu, Weber, Hendrik, and Wulkenhaar, Raimar. 2025. “Stochastic quantization of λϕ^4_2-theory in 2-d Moyal space.” Preprint. arXiv doi: 10.48550/arXiv.2502.02355.
• Melong, Fridolin, and Wulkenhaar, Raimar. 2025. “Characterization of the W_{1+∞}-n-algebra and applications.” International Journal of Modern Physics A 40 (26) 2550103. doi: 10.1142/S0217751X25501039.
• Hock, Alexander, Wulkenhaar, Raimar, and Dołega, Maciej (appendix). 2025. “Blobbed topological recursion of the quartic Kontsevich model II: Genus=0.” Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions 12: 545–619. doi: 10.4171/AIHPD/198.

2024

• Borot, Gaëtan, and Wulkenhaar, Raimar. 2024. “A note on BKP for the Kontsevich matrix model with arbitrary potential.” Symmetry, Integrability and Geometry: Methods and Applications 20 050. doi: 10.3842/SIGMA.2024.050.
• Grosse, Harald, Kanomata, Naoyuki, Sako, Akifumi, and Wulkenhaar, Raimar. 2024. “Real symmetric Φ^4-matrix model as Calogero-Moser model.” Letters in Mathematical Physics 114 25. doi: 10.1007/s11005-024-01772-5.
• Grosse, Harald, Kanomata, Naoyuki, Sako, Akifumi, and Wulkenhaar, Raimar. 2024. “Relationship between Φ^4-matrix model and N-body harmonic oscillator or Calogero-Moser model.” contribution to the The XXVIII International Conference on Integrable Systems and Quantum Symmetries (ISQS28), Prague doi: 10.1088/1742-6596/2912/1/012014.

2023

• Melong, Fridolin, and Wulkenhaar, Raimar. 2023. “Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra.” Journal of Mathematical Physics 64 (7) 073505. doi: 10.1063/5.0150975.
• Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. 2023. “A Laplacian to compute intersection numbers on M_{g,n} and correlation functions in NCQFT.” Communications in Mathematical Physics 399: 481–517. doi: 10.1007/s00220-022-04557-w.
• Schürmann, Jörg, and Wulkenhaar, Raimar. 2023. “An algebraic approach to a quartic analogue of the Kontsevich model.” Mathematical Proceedings 174 (3): 471–495. doi: 10.1017/S0305004122000366.

2022

• Branahl, Johannes, Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. 2022. “From scalar fields on quantum spaces to blobbed topological recursion.” Journal of Physics A: Mathematical and Theoretical 55 (42) 423001. doi: 10.1088/1751-8121/ac9260.
• Branahl, Johannes, Hock, Alexander, and Wulkenhaar, Raimar. 2022. “Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures.” Communications in Mathematical Physics 393: 1529–1582. doi: 10.1007/s00220-022-04392-z.
• de Jong, Jins, Hock, Alexander, and Wulkenhaar, Raimar. 2022. “Nested Catalan tables and a recurrence relation in noncommutative quantum field theory.” Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions 9 (1): 47–72. doi: 10.4171/AIHPD/113.
• Kohl, Finn Bjarne, and Wulkenhaar, Raimar. 2022. “Intersection theory of the complex quartic Kontsevich model.” Preprint. arXiv doi: 10.48550/arXiv.2212.01359.

2021

• Pascalie, Romain, Pérez-Sánchez, Carlos Ignacio, and Wulkenhaar, Raimar. 2021. “Correlation functions of U(N)-tensor models and their Schwinger-Dyson equations.” Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions 8 (3): 377–458. doi: 10.4171/AIHPD/107.
• Branahl, Johannes, Hock, Alexander, and Wulkenhaar, Raimar. 2021. “Perturbative and geometric analysis of the quartic Kontsevich model.” Symmetry, Integrability and Geometry: Methods and Applications 17: 085. doi: 10.3842/SIGMA.2021.085.

2020

• Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. 2020. “Solution of the self-dual \Phi^4 QFT-model on four-dimensional Moyal space.” Journal of High Energy Physics 01: 081.. doi: 10.1007/JHEP01(2020)081.
• Münster, Gernot, and Wulkenhaar, Raimar. 2020. “The Leutwyler-Smilga relation on the lattice.” Modern Physics Letters A 35 (01): 1950346.. doi: 10.1142/S0217732319503462.
• Panzer, Erik, and Wulkenhaar, Raimar. 2020. “Lambert-W solves the noncommutative ϕ4-model.” Communications in Mathematical Physics 374: 1935–1961. doi: 10.1007/s00220-019-03592-4.

2019

• de Jong, Jins, and Wulkenhaar, Raimar. 2019. “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. doi: 10.1063/1.5063293.
• Pascalie, Romain, Pérez-Sánchez, Carlos Ignacio, Tanasa, Adrian, and Wulkenhaar, Raimar. 2019. “On the large N limit of the Schwinger-Dyson equation of rank-3 tensor field theory.” Journal of Mathematical Physics 60 (7) 073502. doi: 10.1063/1.5080306.
• Wulkenhaar, Raimar. 2019. “Quantum field theory on noncommutative spaces.” in Advances in Noncommutative Geometry, edited by Ali Chamseddine, Caterina Consani, Nigel Higson, Masoud Khalkhali, Henri Moscovici and Guoliang Yu. Cham: Springer International Publishing. doi: 10.1007/978-3-030-29597-4_11.

2018

• Grosse, Harald, and Wulkenhaar, Raimar. 2018. “Integrability and positivity in quantum field theory on noncommutative geometry.” Journal of Geometry and Physics 134: 249–262. doi: 10.1016/j.geomphys.2018.08.001.
• Grosse, Harald, and Wulkenhaar, Raimar. 2018. “How Prof. Zeidler supported our research on exact solution of quantum field theory toy models.” Vietnam Journal of Mathematics 47: 93–112. doi: 10.1007/s10013-018-0302-2.
• Hock, Alexander, and Wulkenhaar, Raimar. 2018. “Noncommutative 3-colour scalar quantum field theory model in 2D.” European Physical Journal C: Particles and Fields 78 580. doi: 10.1140/epjc/s10052-018-6042-3.
• Wulkenhaar, Raimar. 2018. “Lambert-W solves the noncommutative \Phi^4-model.” in Vol. 15 of Oberwolfach Reports doi: 10.4171/OWR/2018/32.
• Grosse, Harald, Sako, Akifumi, and Wulkenhaar, Raimar. 2018. “The \Phi^3_4 and \Phi^3_6 matricial QFT models have reflection positive two-point function.” Nuclear Physics B 926: 20–48. doi: 10.1016/j.nuclphysb.2017.10.022.

2017

• Grosse, Harald, Sako, Akifumi, and Wulkenhaar, Raimar. 2017. “Exact solution of matricial \Phi^3_2 quantum field theory.” Nuclear Physics B 925: 319–347. doi: 10.1016/j.nuclphysb.2017.10.010.
• de Jong, Jins, and Wulkenhaar, Raimar. 2017. “The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices.” Preprint. arXiv.org doi: 10.48550/arXiv.1701.07719.
• Wulkenhaar, Raimar. 2017. “Reflection positivity in large-deformation limits of noncommutative field theories.” in Vol. 14 of Oberwolfach Reports doi: 10.4171/OWR/2017/55.

2016

• Wulkenhaar, Raimar. 2016. “Integrability in a 4D QFT model.” in Vol. 13 of Oberwolfach Reports 13 doi: 10.4171/OWR/2016/36.
• Grosse, Harald, and Wulkenhaar, Raimar. 2016. “Construction of a quantum field theory in four dimensions.” PoS - Proceedings of Science 224 151. doi: 10.22323/1.224.0151.
• Grosse, Harald, and Wulkenhaar, Raimar. 2016. “A solvable four-dimensional QFT.” in Quantum Mathematical Physics - A Bridge between Mathematics and Physics, edited by F Finster, J Kleiner, C Röken and J Tolksdorf. Cham Heidelberg New York Dordrecht London: Springer International Publishing. doi: 10.1007/978-3-319-26902-3_8.
• Eckstein, Michał, Sitarz, Andrzej, and Wulkenhaar, Raimar. 2016. “The Moyal sphere.” Journal of Mathematical Physics 2016 (57) 112301. doi: 10.1063/1.4965446.
• Grosse, Harald, and Wulkenhaar, Raimar. 2016. “On the fixed point equation of a solvable 4D QFT model.” Vietnam Journal of Mathematics 44: 153–180. doi: 10.1007/s10013-015-0174-7.

2015

• Ousmane Samary, Dine, Pérez-Sánchez, Carlos Ignacio, Vignes-Tourneret, Fabien, and Wulkenhaar, Raimar. 2015. “Correlation functions of a just renormalizable tensorial group field theory: the melonic approximation.” Classical and Quantum Gravity 32 (17): 175012.. doi: 10.1088/0264-9381/32/17/175012.

2014

• Grosse, Harald, and Wulkenhaar, Raimar. 2014. “Towards a construction of a quantum field theory in four dimensions.” in Mathematical Structures of the Universe, edited by M Eckstein, M Heller and S Szybka. Kraków: Copernicus Center Press.
• Grosse, Harald, and Wulkenhaar, Raimar. 2014. “Noncommutative quantum field theory.” Fortschritte der Physik 62 (9-10): 797–811. doi: 10.1002/prop.201400020.
• Grosse, Harald, and Wulkenhaar, Raimar. 2014. “Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity.” Preprint. arXiv doi: 10.48550/arXiv.1406.7755.
• Grosse, Harald, and Wulkenhaar, Raimar. 2014. “Self-dual noncommutative ϕ4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory.” Communications in Mathematical Physics 329 (3): 1069–1130. doi: 10.1007/s00220-014-1906-3.
• Grosse, Harald, and Wulkenhaar, Raimar. 2014. “Construction of the \Phi^4_4-quantum field theory on noncommutative Moyal space.” RIMS Kôkyûroku 2014 (1904): 67–104.

2013

• Gayral, Victor, and Wulkenhaar, Raimar. 2013. “Spectral geometry of the Moyal plane with harmonic propagation.” Journal of Noncommutative Geometry 7 (4): 939–979. doi: 10.4171/JNCG/140.
• Grosse, Harald, and Wulkenhaar, Raimar. 2013. “Construction and properties of noncommutative quantum fields.” in XVIIth International Congress on Mathematical Physics, edited by A Jensen. Singapore: World Scientific Publishing. doi: 10.1142/9789814449243_0066.
• Grosse, Harald, and Wulkenhaar, Raimar. 2013. “Solvable limits of a 4D noncommutative QFT.” Preprint. arXiv doi: 10.48550/arXiv.1306.2816.
• Grosse, Harald, and Wulkenhaar, Raimar. 2013. “Construction of a Noncommutative Quantum Field Theory.” in Spectral Analysis, Differential Equations and Mathematical Physics: A Festschrift in Honor of Fritz Gesztesy's 60th Birthday, Vol. 87 of Proceedings of Symposia in Pure Mathematics, edited by H Holden, B Simon and G Teschl. Providence, RI: American Mathematical Society. doi: 10.1090/pspum/087/01442.

2012

• Spisso, Bernardino, and Wulkenhaar, Raimar. 2012. “A numerical approach to harmonic non-commutative spectral field theory.” International Journal of Modern Physics A 27 (14) 1250075. doi: 10.1142/S0217751X12500753.
• Grosse, Harald, and Wulkenhaar, Raimar. 2012. “Renormalization of a noncommutative field theory.” International Journal of Modern Physics A 27 (12) 1250067. doi: 10.1142/S0217751X12500674.
• Grosse, Harald, and Wulkenhaar, Raimar. 2012. “8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory.” Journal of Geometry and Physics 62 (7): 1583–1599. doi: 10.1016/j.geomphys.2012.03.005.
• Grosse, Harald, and Wulkenhaar, Raimar. 2012. “Renormalization of a noncommutative field theory.” International Journal of Modern Physics: Conference Series 13: 108–117. doi: 10.1142/S2010194512006770.
• Grosse, Harald, and Wulkenhaar, Raimar. 2012. “Renormalizable noncommutative quantum field theory.” Journal of Physics: Conference Series 343 012043. doi: 10.1088/1742-6596/343/1/012043.

2011

• Grosse, Harald, and Wulkenhaar, Raimar. 2011. “Renormalisation of the Grosse-Wulkenhaar model.” PoS - Proceedings of Science QGQGS (2011) 011.
• Grosse, Harald, and Wulkenhaar, Raimar. 2011. “Renormalizable noncommutative quantum field theory.” General Relativity and Gravitation 43: 2491–2498. doi: 10.1007/s10714-010-1065-6.

2010

• Wulkenhaar, Raimar. 2010. “Quantum field theory on noncommutative geometries.” in Vol. 7 of Oberwolfach Reports doi: 10.4171/OWR/2010/09.
• Wulkenhaar, Raimar. 2010. “Non-compact spectral triples with finite volume.” in Quanta of Maths, Vol. 11 of Clay Math. Proc., edited by E Blanchard, D Ellwood, M Khalkhali, M Marcolli, H Moscovici and S Popa. Providence, RI: American Mathematical Society.

2009

• Wulkenhaar, Raimar. 2009. “Progress in solving a noncommutative QFT in four dimensions.” in Vol. 6 of Oberwolfach Reports doi: 10.4171/OWR/2009/41.
• Grosse, Harald, and Wulkenhaar, Raimar. 2009. “Progress in solving a noncommutative quantum field theory in four dimensions.” Preprint. arXiv doi: 10.48550/arXiv.0909.1389.

2008

• Grosse, Harald, and Wulkenhaar, Raimar. 2008. “Renormalization of noncommutative quantum field theory.” in An invitation to noncommutative geometry, edited by M Khalkhali and M Marcolli. Singapore: World Scientific Publishing. doi: 10.1142/9789812814333_0002.
• Marcillaud de Goursac, Axel, Wallet, Jean-Christophe, and Wulkenhaar, Raimar. 2008. “On the vacuum states for non-commutative gauge theory.” European Physical Journal C: Particles and Fields 56 (2): 293–304. doi: 10.1140/epjc/s10052-008-0652-0.

2007

• Gayral, Victor, Jureit, Jan-Hendrik, Krajewski, Thomas, and Wulkenhaar, Raimar. 2007. “Quantum field theory on projective modules.” Journal of Noncommutative Geometry 1 (4): 431–496. doi: 10.4171/JNCG/13.
• Marcillaud de Goursac, Axel, Wallet, Jean-Christophe, and Wulkenhaar, Raimar. 2007. “Noncommutative induced gauge theory.” European Physical Journal C: Particles and Fields 51 (4): 977–987. doi: 10.1140/epjc/s10052-007-0335-2.
• Wulkenhaar, Raimar. 2007. “The harmonic oscillator, its noncommutative dimension and the vacuum of noncommutative gauge theory.” in Vol. 4 of Oberwolfach Reports doi: 10.4171/OWR/2007/43.
• Grosse, Harald, and Wulkenhaar, Raimar. 2007. “Noncommutative QFT and renormalization.” in Quantum Gravity - Mathematical Models and Experimental Bounds, edited by B Fauser, J Tolksdorf and E Zeidler. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-7643-7978-0_16.

2006

• Wulkenhaar, Raimar. 2006. “Renormalisation scalar quantum field theory on 4D-Moyal plane.” in Vol. 3 of Oberwolfach Reports doi: 10.4171/OWR/2006/17.
• Grosse, Harald, and Wulkenhaar, Raimar. 2006. “Noncommutative QFT and renormalization.” Fortschritte der Physik 54 (2-3): 116–123. doi: 10.1002/prop.200510260.
• Grosse, Harald, and Wulkenhaar, Raimar. 2006. “Noncommutative QFT and renormalization.” Bulgarian Journal of Physics 33 (s1): 215–225.
• Rivasseau, Vincent, Vignes-Tourneret, Fabien, and Wulkenhaar, Raimar. 2006. “Renormalisation of noncommutative ϕ4-theory by multi-scale analysis.” Communications in Mathematical Physics 262 (3): 565–594. doi: 10.1007/s00220-005-1440-4.
• Wulkenhaar, Raimar. 2006. “Field theories on deformed spaces.” Journal of Geometry and Physics 56 (1): 108–141. doi: 10.1016/j.geomphys.2005.04.019.

2005

• Grosse, Harald, and Wulkenhaar, Raimar. 2005. “Power-counting theorem for non-local matrix models and renormalisation.” Communications in Mathematical Physics 254 (1): 91–127. doi: 10.1007/s00220-004-1238-9.
• Wulkenhaar, R. 2005. “Euclidean quantum field theory on commutative and noncommutative spaces.” in Geometric and Topological Methods for Quantum Field Theory, Vol. 668 of Lecture Notes in Physics, edited by H Ocampo, S Paycha and A Vargas. Berlin: Springer VDI Verlag. doi: 10.1007/11374060_2.
• Grosse, Harald, and Wulkenhaar, Raimar. 2005. “Renormalisation of ϕ4-Theory on Noncommutative ℝ4 in the Matrix Base.” Communications in Mathematical Physics 256 (2): 305–374. doi: 10.1007/s00220-004-1285-2.
• Grosse, H, and Wulkenhaar, R. 2005. “Renormalisation of scalar quantum field theory on noncommutative R^4.” Fortschritte der Physik 53 (5-6): 634–639. doi: 10.1002/prop.200410231.
• Grosse, H, and Wulkenhaar, R. 2005. “Renormalisation of \phi^4-theory on non-commutative R^4 to all orders.” Letters in Mathematical Physics 71 (1): 13–26. doi: 10.1007/s11005-004-5116-3.

2004

• Wulkenhaar, R. 2004. “Renormalisation of noncommutative \phi^4-theory to all orders.” in Vol. 1 of Oberwolfach Reports doi: 10.4171/OWR/2004/45.
• Grosse, H, and Wulkenhaar, R. 2004. “Renormalisation group approach to noncommutative quantum field theory.” in Particle Physics and the Universe, Vol. 98 of Springer Proceedings in Physics, edited by J Trampetic and J Wess. Springer VDI Verlag. doi: 10.1007/3-540-26798-0_19.
• Grosse, H, and Wulkenhaar, R. 2004. “Renormalisation of noncommutative scalar field theories.” in Lie Theory and its Applications in Physics V, edited by H-D Doebner and VK Dobrev. World Scientific Publishing. doi: 10.1142/9789812702562_0006.
• Grosse, H, and Wulkenhaar, R. 2004. “Renormalisation of noncommutative quantum field theories.” Czechoslovak Journal of Physics 54 (11): 1305–1311. doi: 10.1007/s10582-004-9793-z.
• Grosse, H, and Wulkenhaar, R. 2004. “Regularization and renormalization of quantum field theories on noncommutative spaces.” Journal of Nonlinear Mathematical Physics 11 (suppl.): 9–20. doi: 10.2991/jnmp.2004.11.s1.2.
• Bichl, AA, Ertl, M, Gerhold, A, Grimstrup, JM, Popp, L, Putz, V, Schweda, M, Grosse, H, and Wulkenhaar, R. 2004. “Noncommutative U(1) super-Yang-Mills theory: perturbative self-energy corrections.” International Journal of Modern Physics A 19 (25): 4231–4249. doi: 10.1142/S0217751X04018221.
• Grimstrup, JM, Grosse, H, Popp, L, Putz, V, Schweda, M, Wickenhauser, M, and Wulkenhaar, R. 2004. “IR singularities in noncommutative perturbative dynamics?” Europhysics Letters 67 (2): 186–190. doi: 10.1209/epl/i2003-10285-9.
• Grosse, Harald, and Wulkenhaar, Raimar. 2004. “The \beta-function in duality-covariant non-commutative \phi^4-theory.” European Physical Journal C: Particles and Fields 35 (2): 277–282. doi: 10.1140/epjc/s2004-01853-x.

2003

• Grosse, H, and Wulkenhaar, R. 2003. “Regularisation and renormalisation of quantum field theories on noncommutative spaces.” in Modern Mathematical Physics, edited by B Dragovich and B Sazdovic. Belgrade Institute of Physics.
• Grosse, H, and Wulkenhaar, R. 2003. “Renormalisation of \phi^4-theory on noncommutative R^2 in the matrix base.” Journal of High Energy Physics 03 (12): 019.. doi: 10.1088/1126-6708/2003/12/019.
• Putz, V, and Wulkenhaar, R. 2003. “Seiberg-Witten map for noncommutative super Yang-Mills theory.” International Journal of Modern Physics A 18 (19): 3325–3334. doi: 10.1142/S0217751X03015246.
• Bozkaya, H, Fischer, P, Grosse, H, Pitschmann, M, Putz, V, Schweda, M, and Wulkenhaar, R. 2003. “Space/time non-commutative field theories and causality.” European Physical Journal C: Particles and Fields 29 (1): 133–141. doi: 10.1140/epjc/s2003-01210-9.

2002

• Martinetti, P, and Wulkenhaar, R. 2002. “Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry.” Journal of Mathematical Physics 43 (1): 182–204. doi: 10.1063/1.1418012.
• Wulkenhaar, R. 2002. Quantum field theories on noncommutative R^4 versus \theta-expanded quantum field theories
• Bichl, AA, Grimstrup, JM, Grosse, H, Kraus, E, Popp, L, Schweda, M, and Wulkenhaar, R. 2002. “Noncommutative Lorentz symmetry and the origin of the Seiberg-Witten map.” European Physical Journal C 24: 491–494. doi: 10.1007/s100520100857.
• Grimstrup, JM, and Wulkenhaar, R. 2002. “Quantisation of \theta-expanded non-commutative QED.” European Physical Journal C: Particles and Fields 26 (1): 139–151. doi: 10.1140/epjc/s2002-01038-9.
• Gerhold, A, Grimstrup, J, Grosse, H, Popp, L, Schweda, M, and Wulkenhaar, R. 2002. “The energy-momentum tensor on noncommutative spaces -- some pedagogical comments.” Ukrainian Journal of Physics 47 (3): 219–225.
• Grimstrup, JM, Grosse, H, Kraus, E, Popp, L, Schweda, M, and Wulkenhaar, R. 2002. “Noncommutative spin-1/2 representations.” European Physical Journal C: Particles and Fields 24 (3): 491–494. doi: 10.1007/s10052-002-0938-6.
• Bichl, AA, Grimstrup, JM, Popp, L, Schweda, M, and Wulkenhaar, R. 2002. “Perturbative analysis of the Seiberg-Witten map.” International Journal of Modern Physics A 17 (16): 2219–2231. doi: 10.1142/S0217751X02010649.
• Wulkenhaar, R. 2002. “Non-renormalizability of \theta-expanded non-commutative QED.” Journal of High Energy Physics 02 (03): 024.. doi: 10.1088/1126-6708/2002/03/024.
• Wulkenhaar, R. 2002. “Introduction to Hopf algebras in renormalization and noncommutative geometry.” in Noncommutative geometry and the standard model of elementary particle physics, Vol. 596 of Lecture Notes in Physics, edited by F Scheck, H Upmeier and W Werner. Berlin: Springer VDI Verlag. doi: 10.1007/3-540-46082-9_17.

2001

• Bichl, AA, Grimstrup, JM, Popp, L, Schweda, M, and Wulkenhaar, R. 2001. Deformed QED via Seiberg-Witten map
• Bichl, AA, Grimstrup, JM, Popp, L, Schweda, M, Grosse, H, and Wulkenhaar, R. 2001. “Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map.” Journal of High Energy Physics 01 (06): 013.. doi: 10.1088/1126-6708/2001/06/013.

2000

• Krajewski, Thomas, and Wulkenhaar, Raimar. 2000. “Perturbative quantum gauge fields on the noncommutative torus.” International Journal of Modern Physics A 15 (7): 1011–1029. doi: 10.1142/S0217751X00000495.
• Grosse, H, Krajewski, T, and Wulkenhaar, R. 2000. Renormalization of noncommutative Yang-Mills theories: A simple example
• Wulkenhaar, R. 2000. “Slavnov-Taylor identity in noncommutative geometry.” International Journal of Modern Physics B 14 (22-23): 2503–2509. doi: 10.1142/S0217979200002053.
• Bichl, AA, Grimstrup, JM, Popp, L, Schweda, M, Grosse, H, and Wulkenhaar, R. 2000. “The superfield formalism applied to the non-commutative Wess-Zumino model.” Journal of High Energy Physics 00 (10): 046.. doi: 10.1088/1126-6708/2000/10/046.

1999

• Wulkenhaar, R. 1999. On the Connes-Moscovici Hopf algebra associated to the diffeomorphisms of a manifold
• Wulkenhaar, R. 1999. “Gauge theories with graded differential Lie algebras.” Journal of Mathematical Physics 40 (2): 787–794. doi: 10.1063/1.532685.
• Wulkenhaar, R. 1999. “On Feynman graphs as elements of a Hopf algebra.” in Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions, Vol. 226 of Horizons in World Physics, edited by D Kastler, M Rosso and T Schücker. Nova Science Publishers.
• Krajewski, T, and Wulkenhaar, R. 1999. “On Kreimer's Hopf algebra structure of Feynman graphs.” European Physical Journal C: Particles and Fields 7 (4): 697–708. doi: 10.1007/s100520050439.
• Wulkenhaar, R. 1999. “SO(10)-unification in noncommutative geometry revisited.” International Journal of Modern Physics A 14 (4): 559–588. doi: 10.1142/S0217751X99000282.

1998

• Wulkenhaar, R. 1998. “Graded differential Lie algebras and SU(5) x U(1)-grand unification.” International Journal of Modern Physics A 13 (15): 2627–2692. doi: 10.1142/S0217751X98001359.
• Wulkenhaar, R. 1998. “Graded differential Lie algebras and model building.” Journal of Geometry and Physics 25 (3-4): 305–325. doi: 10.1016/S0393-0440(97)00029-6.
• Wulkenhaar, R. 1998. “Gauge field theories in terms of graded differential Lie algebras.” in Lie Theory and its Applications in Physics II, edited by H-D Doebner, VK Dobrev and J Hilgert. World Scientific Publishing. doi: 10.1142/3852.

1997

• Wulkenhaar, R. 1997. Gyros as geometry of the standard model
• Wulkenhaar, R. 1997. “Noncommutative geometry with graded differential Lie algebras.” Journal of Mathematical Physics 38 (6): 3358–3390. doi: 10.1063/1.532048.
• Wulkenhaar, R. 1997. “The standard model within non-associative geometry.” Physics Letters B 390 (1-4): 119–127. doi: 10.1016/S0370-2693(96)01336-6.
• Wulkenhaar, R. 1997. “Yang-Mills-Higgs models arising from L-cycles.” in GROUP 21, edited by H-D Doebner, P Nattermann, W Scherer and C Schulte. World Scientific Publishing. doi: 10.1142/3473.

1996

• Matthes, R, Rudolph, G, and Wulkenhaar, R. 1996. “Graded Lie algebras with derivation and model building.” in Lie Theory and its Applications in Physics, edited by H-D Doebner, VK Dobrev and J Hilgert. World Scientific Publishing. doi: 10.1142/3301.
• Matthes, R, Rudolph, G, and Wulkenhaar, R. 1996. “On certain graded Lie algebras arising in noncommutative geometry.” Acta Physica Polonica Series B 27 (10): 2755–2762.
• Matthes, R, Rudolph, G, and Wulkenhaar, R. 1996. “On the structure of a differential algebra used by Connes and Lott.” Reports on Mathematical Physics 38 (1): 45–66. doi: 10.1016/0034-4877(96)87677-4.
• Matthes, R, Rudolph, G, and Wulkenhaar, R. 1996. “On a certain construction of graded Lie algebras with derivation.” Journal of Geometry and Physics 20 (2-3): 107–141. doi: 10.1016/0393-0440(95)00048-8.
• Wulkenhaar, R. 1996. “Deriving the standard model from the simplest two-point K-cycle.” Journal of Mathematical Physics 37 (8): 3797–3814. doi: 10.1063/1.531602.