Professor Dr. Raimar Wulkenhaar

Professur für Reine Mathematik (Prof. Wulkenhaar)

Einsteinstr. 62
48149 Münster

Academic Profile

  • Research Areas

    • Mathematical Physics
    • Quantum field theory
    • Noncommutative geometry

  • CV

    Education

    Habilitation in Physics, Technical University Vienna
    Dissertation in Physics, University of Leipzig (Prof. G. Rudolph)
    Study of Physics, University of Leipzig, Diploma Physics (Prof. G. Rudolph)
    Study of Physics, Otto-von-Guericke-University Magdeburg, Pre-diploma

    Positions

    Professor (W2) for Pure Mathematics, WWU Münster
    Maître de Conférence invité, Université de Provence, Marseille
    Scientific Assistant, Max-Planck-Institute for Mathematics in the Sciences, Leipzig
    Marie-Curie Fellow, Faculty of Physics, University of Vienna
    DAAD Postdoc Fellow, Centre de Physique Théorique, Marseille

    External Functions

    Member of the Editorial Board of the Journal of Noncommutative Geometry
    Principal Investigator in Cluster of Excellence "Mathematics Münster"
    Member of the Editorial Board of Annales Henri Poincaré
    Member of the German Physical Society
    Member of the German National Scholarship Foundation

  • Publications

    Selection

    • Schürmann, Jörg; Wulkenhaar, Raimar. . ‘An algebraic approach to a quartic analogue of the Kontsevich model.’ Mathematical Proceedings 174, No. 3: 471–495. doi: 10.1017/S0305004122000366.

    • Branahl, Johannes; Hock, Alexander; Wulkenhaar, Raimar. . ‘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.

    • Panzer, Erik; Wulkenhaar, Raimar. . ‘Lambert-W solves the noncommutative \Phi^4-model.’ Communications in Mathematical Physics 374: 1935–1961. doi: 10.1007/s00220-019-03592-4.

    • Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar. . Solution of all quartic matrix models arXiv. doi: 10.48550/arXiv.1906.04600. [submitted / under review]
    • Wulkenhaar, Raimar. . ‘Quantum field theory on noncommutative spaces.’ In Advances in Noncommutative Geometry, edited by Chamseddine, A; Consani, C; Higson, N; Khalkhali, M; Moscovici, H; Yu, G, 607–690. Cham: Springer International Publishing. doi: 10.1007/978-3-030-29597-4_11.

    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory.’ Communications in Mathematical Physics 329, No. 3: 1069–1130. doi: 10.1007/s00220-014-1906-3.

    • Rivasseau, Vincent, Vignes-Tourneret, Fabien; Wulkenhaar, Raimar. . ‘Renormalisation of noncommutative \phi^4-theory by multi-scale analysis.’ Communications in Mathematical Physics 262, No. 3: 565–594. doi: 10.1007/s00220-005-1440-4.

    • Grosse H, Wulkenhaar R. . ‘Power-counting theorem for non-local matrix models and renormalisation.’ Communications in Mathematical Physics 254, No. 1: 91–127. doi: 10.1007/s00220-004-1238-9.
    • Grosse H, Wulkenhaar R. . ‘Renormalisation of \phi^4-theory on noncommutative R^4 in the matrix base .’ Communications in Mathematical Physics 256, No. 2: 305–374. doi: 10.1007/s00220-004-1285-2.

    • Krajewski T, Wulkenhaar R. . ‘Perturbative quantum gauge fields on the noncommutative torus.’ International Journal of Modern Physics A 15, No. 7: 1011–1029. doi: 10.1142/S0217751X00000495.

    Complete List

    • Borot, Gaëtan; Wulkenhaar, Raimar. . A short note on BKP for the Kontsevich matrix model with arbitrary potential arXiv. doi: 10.48550/arXiv.2306.01501. [submitted / under review]
    • Melong, Fridolin; Wulkenhaar, Raimar. . ‘Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra.’ Journal of Mathematical Physics : 2303.08073. doi: 10.48550/arXiv.2303.08073. [accepted / in press (not yet published)]
    • Hock, Alexander; Wulkenhaar, Raimar. . Blobbed topological recursion from extended loop equations arXiv. doi: 10.48550/arXiv.2301.04068. [submitted / under review]
    • 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 399: 481–517. doi: 10.1007/s00220-022-04557-w.
    • Schürmann, Jörg; Wulkenhaar, Raimar. . ‘An algebraic approach to a quartic analogue of the Kontsevich model.’ Mathematical Proceedings 174, No. 3: 471–495. doi: 10.1017/S0305004122000366.

    • Branahl, Johannes; Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar. . ‘From scalar fields on quantum spaces to blobbed topological recursion.’ Journal of Physics A: Mathematical and Theoretical 55, No. 42: 423001. doi: 10.1088/1751-8121/ac9260.
    • Branahl, Johannes; Hock, Alexander; Wulkenhaar, Raimar. . ‘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; Wulkenhaar, Raimar. . ‘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, No. 1: 47–72. doi: 10.4171/AIHPD/113.
    • Kohl, Finn Bjarne; Wulkenhaar, Raimar. . Intersection theory of the complex quartic Kontsevich model arXiv. doi: 10.48550/arXiv.2212.01359. [submitted / under review]

    • Pascalie, Romain; Pérez-Sánchez, Carlos Ignacio, Wulkenhaar, Raimar. . ‘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, No. 3: 377–458. doi: 10.4171/AIHPD/107.
    • Branahl, Johannes; Hock, Alexander; Wulkenhaar, Raimar. . ‘Perturbative and geometric analysis of the quartic Kontsevich model.’ Symmetry, Integrability and Geometry: Methods and Applications 17: 085. doi: 10.3842/SIGMA.2021.085.
    • Hock, Alexander; Wulkenhaar, Raimar. . Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 arXiv. doi: 10.48550/arXiv.2103.13271. [submitted / under review]

    • Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar. . ‘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; Wulkenhaar, Raimar. . ‘The Leutwyler-Smilga relation on the lattice.’ Modern Physics Letters A 35, No. 01: 1950346. doi: 10.1142/S0217732319503462.
    • Panzer, Erik; Wulkenhaar, Raimar. . ‘Lambert-W solves the noncommutative \Phi^4-model.’ Communications in Mathematical Physics 374: 1935–1961. doi: 10.1007/s00220-019-03592-4.

    • de Jong, Jins; Wulkenhaar, Raimar. . ‘Nonperturbative evaluation of the partition function for the real scalar quartic QFT on the Moyal plane at weak coupling.’ Journal of Mathematical Physics 60, No. 8: 083504. doi: 10.1063/1.5063293.
    • Pascalie, Romain; Pérez-Sánchez, Carlos Ignacio; Tanasa, Adrian; Wulkenhaar, Raimar. . ‘On the large N limit of the Schwinger-Dyson equation of rank-3 tensor field theory.’ Journal of Mathematical Physics 60, No. 7: 073502. doi: 10.1063/1.5080306.
    • Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar. . Solution of all quartic matrix models arXiv. doi: 10.48550/arXiv.1906.04600. [submitted / under review]
    • Wulkenhaar, Raimar. . ‘Quantum field theory on noncommutative spaces.’ In Advances in Noncommutative Geometry, edited by Chamseddine, A; Consani, C; Higson, N; Khalkhali, M; Moscovici, H; Yu, G, 607–690. Cham: Springer International Publishing. doi: 10.1007/978-3-030-29597-4_11.

    • Grosse, Harald; Wulkenhaar, Raimar. . ‘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; Wulkenhaar, Raimar. . ‘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; Wulkenhaar, Raimar. . ‘Noncommutative 3-colour scalar quantum field theory model in 2D.’ European Physical Journal C 78: 580. doi: 10.1140/epjc/s10052-018-6042-3.
    • Wulkenhaar, Raimar. . ‘Lambert-W solves the noncommutative \Phi^4-model.’ Contributed to the Non-commutative Geometry, Index Theory and Mathematical Physics, Oberwolfach. doi: 10.4171/OWR/2018/32.
    • Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar. . ‘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.

    • Grosse, Harald; Sako, Akifumi; Wulkenhaar, Raimar. . ‘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; Wulkenhaar, Raimar. . The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices arXiv.org. doi: 10.48550/arXiv.1701.07719. [submitted / under review]
    • Wulkenhaar, Raimar. . ‘Reflection positivity in large-deformation limits of noncommutative field theories.’ Contributed to the Reflection Positivity, Oberwolfach. doi: 10.4171/OWR/2017/55.

    • Wulkenhaar, Raimar. . ‘Integrability in a 4D QFT model.’ Contributed to the Recent Mathematical Developments in Quantum Field Theory, Oberwolfach. doi: 10.4171/OWR/2016/36.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Construction of a quantum field theory in four dimensions.’ PoS - Proceedings of Science 224: 151. doi: 10.22323/1.224.0151.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘A solvable four-dimensional QFT.’ In Quantum Mathematical Physics - A Bridge between Mathematics and Physics, edited by Finster, F; Kleiner, J; Röken, C; Tolksdorf, J, 153–180. Cham Heidelberg New York Dordrecht London: Springer International Publishing. doi: 10.1007/978-3-319-26902-3_8.
    • Eckstein, Michał; Sitarz, Andrzej; Wulkenhaar, Raimar. . ‘The Moyal sphere.’ Journal of Mathematical Physics 2016, No. 57: 112301. doi: 10.1063/1.4965446.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘On the fixed point equation of a solvable 4D QFT model.’ Vietnam Journal of Mathematics 2016, No. 44: 153–180. doi: 10.1007/s10013-015-0174-7.

    • Ousmane Samary, Dine; Pérez-Sánchez, Carlos Ignacio; Vignes-Tourneret, Fabien; Wulkenhaar, Raimar. . ‘Correlation functions of a just renormalizable tensorial group field theory: the melonic approximation.’ Classical and Quantum Gravity 32, No. 17: 175012. doi: 10.1088/0264-9381/32/17/175012.

    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Towards a construction of a quantum field theory in four dimensions.’ In Mathematical Structures of the Universe, edited by Eckstein, M; Heller, M; Szybka, S, 227–258. Kraków: Copernicus Center Press.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Noncommutative quantum field theory.’ Fortschritte der Physik 62, No. 9-10: 797–811. doi: 10.1002/prop.201400020.
    • Grosse, Harald; Wulkenhaar, Raimar. . Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity arXiv. doi: 10.48550/arXiv.1406.7755. [submitted / under review]
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory.’ Communications in Mathematical Physics 329, No. 3: 1069–1130. doi: 10.1007/s00220-014-1906-3.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Construction of the \Phi^4_4-quantum field theory on noncommutative Moyal space.’ RIMS Kôkyûroku 2014, No. 1904: 67–104.

    • Gayral, Victor; Wulkenhaar, Raimar. . ‘Spectral geometry of the Moyal plane with harmonic propagation.’ Journal of Noncommutative Geometry 7, No. 4: 939–979. doi: 10.4171/JNCG/140.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Construction and properties of noncommutative quantum fields.’ In XVIIth International Congress on Mathematical Physics, edited by Jensen, A, 643–650. Singapore: World Scientific Publishing. doi: 10.1142/9789814449243_0066.
    • Grosse, Harald; Wulkenhaar, Raimar. . Solvable limits of a 4D noncommutative QFT arXiv. doi: 10.48550/arXiv.1306.2816. [submitted / under review]
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘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, edited by Holden, H; Simon, B; Teschl, G, 153–163. Providence, RI: American Mathematical Society. doi: 10.1090/pspum/087/01442.

    • Spisso, Bernardino; Wulkenhaar, Raimar. . ‘A numerical approach to harmonic non-commutative spectral field theory.’ International Journal of Modern Physics A 27, No. 14: 1250075. doi: 10.1142/S0217751X12500753.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Renormalization of a noncommutative field theory.’ International Journal of Modern Physics A 27, No. 12: 1250067. doi: 10.1142/S0217751X12500674.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘8D-spectral triple on 4D-Moyal space and the vacuum of noncommutative gauge theory.’ Journal of Geometry and Physics 62, No. 7: 1583–1599. doi: 10.1016/j.geomphys.2012.03.005.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Renormalization of a noncommutative field theory.’ International Journal of Modern Physics: Conference Series 13: 108–117. doi: 10.1142/S2010194512006770.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Renormalizable noncommutative quantum field theory.’ Journal of Physics: Conference Series 343: 012043. doi: 10.1088/1742-6596/343/1/012043.

    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Renormalisation of the Grosse-Wulkenhaar model.’ PoS - Proceedings of Science QGQGS, No. 2011: 011.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Renormalizable noncommutative quantum field theory.’ General Relativity and Gravitation 43: 2491–2498. doi: 10.1007/s10714-010-1065-6.

    • Wulkenhaar, Raimar. . ‘Quantum field theory on noncommutative geometries.’ Contributed to the Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples, Oberwolfach. doi: 10.4171/OWR/2010/09.
    • Wulkenhaar, Raimar. . ‘Non-compact spectral triples with finite volume.’ In Quanta of Maths, edited by Blanchard, E; Ellwood, D; Khalkhali, M; Marcolli, M; Moscovici, H; Popa, S, 617–648. Providence, RI: American Mathematical Society.

    • Wulkenhaar, Raimar. . ‘Progress in solving a noncommutative QFT in four dimensions.’ Contributed to the Noncommutative Geometry, Oberwolfach. doi: 10.4171/OWR/2009/41.
    • Grosse, Harald; Wulkenhaar, Raimar. . Progress in solving a noncommutative quantum field theory in four dimensions arXiv. doi: 10.48550/arXiv.0909.1389. [submitted / under review]

    • Marcillaud de Goursac A, Wallet JC, Wulkenhaar R. . ‘On the vacuum states for non-commutative gauge theory.’ European Physical Journal C: Particles and Fields 56, No. 2: 293–304. doi: 10.1140/epjc/s10052-008-0652-0.
    • Grosse, Harald; Wulkenhaar,, Raimar. . ‘Renormalization of noncommutative quantum field theory.’ In An invitation to noncommutative geometry, edited by Khalkhali, M; Marcolli, M, 129–168. Singapore: World Scientific Publishing. doi: 10.1142/9789812814333_0002.

    • Gayral, Victor; Jureit, Jan-Hendrik; Krajewski, Thomas; Wulkenhaar, Raimar. . ‘Quantum field theory on projective modules.’ Journal of Noncommutative Geometry 1, No. 4: 431–496. doi: 10.4171/JNCG/13.
    • Marcillaud de Goursac, Axel; Wallet Jean-Christophe; Wulkenhaar, Raimar. . ‘Noncommutative induced gauge theory.’ European Physical Journal C: Particles and Fields 51, No. 4: 977–987. doi: 10.1140/epjc/s10052-007-0335-2.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Noncommutative QFT and renormalization.’ In Quantum Gravity - Mathematical Models and Experimental Bounds, edited by Fauser, B; Tolksdorf, J; Zeidler, E, 315–326. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-7643-7978-0_16.
    • Wulkenhaar, Raimar. . ‘The harmonic oscillator, its noncommutative dimension and the vacuum of noncommutative gauge theory.’ Contributed to the Noncommutative Geometry, Oberwolfach. doi: 10.4171/OWR/2007/43.

    • Wulkenhaar, Raimar. . ‘Renormalisation scalar quantum field theory on 4D-Moyal plane.’ Contributed to the The Rigorous Renormalization Group, Oberwolfach. doi: 10.4171/OWR/2006/17.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Noncommutative QFT and renormalization.’ Fortschritte der Physik 54, No. 2-3: 116–123. doi: 10.1002/prop.200510260.
    • Grosse, Harald; Wulkenhaar, Raimar. . ‘Noncommutative QFT and renormalization.’ Bulgarian Journal of Physics 33, No. s1: 215–225.
    • Rivasseau, Vincent, Vignes-Tourneret, Fabien; Wulkenhaar, Raimar. . ‘Renormalisation of noncommutative \phi^4-theory by multi-scale analysis.’ Communications in Mathematical Physics 262, No. 3: 565–594. doi: 10.1007/s00220-005-1440-4.
    • Wulkenhaar, Raimar. . ‘Field theories on deformed spaces.’ Journal of Geometry and Physics 56, No. 1: 108–141. doi: 10.1016/j.geomphys.2005.04.019.

    • Grosse H, Wulkenhaar R. . ‘Power-counting theorem for non-local matrix models and renormalisation.’ Communications in Mathematical Physics 254, No. 1: 91–127. doi: 10.1007/s00220-004-1238-9.
    • Wulkenhaar R. . ‘Euclidean quantum field theory on commutative and noncommutative spaces.’ In Geometric and Topological Methods for Quantum Field Theory, edited by Ocampo H, Paycha S, Vargas A, 59––100. Berlin: Springer VDI Verlag. doi: 10.1007/11374060_2.
    • Grosse H, Wulkenhaar R. . ‘Renormalisation of \phi^4-theory on noncommutative R^4 in the matrix base .’ Communications in Mathematical Physics 256, No. 2: 305–374. doi: 10.1007/s00220-004-1285-2.
    • Grosse H, Wulkenhaar R. . ‘Renormalisation of scalar quantum field theory on noncommutative R^4 .’ Fortschritte der Physik 53, No. 5-6: 634––639. doi: 10.1002/prop.200410231.
    • Grosse H, Wulkenhaar R. . ‘Renormalisation of \phi^4-theory on non-commutative R^4 to all orders .’ Letters in Mathematical Physics 71, No. 1: 13––26. doi: 10.1007/s11005-004-5116-3.

    • Grosse H, Wulkenhaar R. . ‘Renormalisation of noncommutative scalar field theories.’ In Lie Theory and its Applications in Physics V, edited by Doebner H-D, Dobrev V K, 109–123. World Scientific Publishing. doi: 10.1142/9789812702562_0006.
    • Grosse H, Wulkenhaar R. . ‘Renormalisation of noncommutative quantum field theories.’ Czechoslovak Journal of Physics 54, No. 11: 1305–1311. doi: 10.1007/s10582-004-9793-z.
    • Grosse H, Wulkenhaar R. . ‘Regularization and renormalization of quantum field theories on noncommutative spaces .’ Journal of Nonlinear Mathematical Physics 11, No. suppl.: 9–20. doi: 10.2991/jnmp.2004.11.s1.2.
    • Bichl A A, Ertl M, Gerhold A, Grimstrup J M, Popp L, Putz V, Schweda M, Grosse H, Wulkenhaar R. . ‘Noncommutative U(1) super-Yang-Mills theory: perturbative self-energy corrections .’ International Journal of Modern Physics A 19, No. 25: 4231–4249. doi: 10.1142/S0217751X04018221.
    • Grimstrup J M, Grosse H, Popp L, Putz V, Schweda M, Wickenhauser M, Wulkenhaar R. . ‘IR singularities in noncommutative perturbative dynamics?’ Europhysics Letters 67, No. 2: 186–190. doi: 10.1209/epl/i2003-10285-9.
    • Grosse H, Wulkenhaar R. . ‘The \beta-function in duality-covariant non-commutative \phi^4-theory.’ European Physical Journal C: Particles and Fields 35, No. 2: 277–282. doi: 10.1140/epjc/s2004-01853-x.
    • Wulkenhaar R. ‘ Renormalisation of noncommutative \phi^4-theory to all orders.’ contributed to the Nichtkommutative Geometrie, Oberwolfach, . doi: 10.4171/OWR/2004/45.
    • Grosse H, Wulkenhaar R. . ‘Renormalisation group approach to noncommutative quantum field theory.’ In Particle Physics and the Universe, edited by Trampetic J, Wess J, 197–208. Springer VDI Verlag. doi: 10.1007/3-540-26798-0_19.

    • Grosse H, Wulkenhaar R. . ‘Renormalisation of \phi^4-theory on noncommutative R^2 in the matrix base .’ Journal of High Energy Physics 03, No. 12: 019. doi: 10.1088/1126-6708/2003/12/019.
    • Putz V, Wulkenhaar R. . ‘Seiberg-Witten map for noncommutative super Yang-Mills theory.’ International Journal of Modern Physics A 18, No. 19: 3325–3334. doi: 10.1142/S0217751X03015246.
    • Bozkaya H, Fischer P, Grosse H, Pitschmann M, Putz V, Schweda M, Wulkenhaar R. . ‘Space/time non-commutative field theories and causality.’ European Physical Journal C: Particles and Fields 29, No. 1: 133–141. doi: 10.1140/epjc/s2003-01210-9.
    • Grosse H, Wulkenhaar R. . ‘Regularisation and renormalisation of quantum field theories on noncommutative spaces.’ In Modern Mathematical Physics, edited by Dragovich B, Sazdovic B, 29–46.: Belgrade Institute of Physics.

    • Martinetti P, Wulkenhaar R. . ‘Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry.’ Journal of Mathematical Physics 43, No. 1: 182–204. doi: 10.1063/1.1418012.
    • Wulkenhaar R. . ‘Introduction to Hopf algebras in renormalization and noncommutative geometry.’ In Noncommutative geometry and the standard model of elementary particle physics, edited by Scheck F, Upmeier H, Werner W, 313–324. Berlin: Springer VDI Verlag. doi: 10.1007/3-540-46082-9_17.
    • Grimstrup J M, Wulkenhaar R. . ‘Quantisation of \theta-expanded non-commutative QED.’ European Physical Journal C: Particles and Fields 26, No. 1: 139–151. doi: 10.1140/epjc/s2002-01038-9.
    • Gerhold A, Grimstrup J, Grosse H, Popp L, Schweda M, Wulkenhaar R. . ‘The energy-momentum tensor on noncommutative spaces -- some pedagogical comments .’ Ukrainian Journal of Physics 47, No. 3: 219–225.
    • Grimstrup J M, Grosse H, Kraus E, Popp L, Schweda M, Wulkenhaar R. . ‘Noncommutative spin-1/2 representations.’ European Physical Journal C: Particles and Fields 24, No. 3: 491––494. doi: 10.1007/s10052-002-0938-6.
    • Bichl A A, Grimstrup J M, Popp L, Schweda M, Wulkenhaar R. . ‘Perturbative analysis of the Seiberg-Witten map.’ International Journal of Modern Physics A 17, No. 16: 2219–2231. doi: 10.1142/S0217751X02010649.
    • Wulkenhaar R. . ‘Non-renormalizability of \theta-expanded non-commutative QED.’ Journal of High Energy Physics 02, No. 03: 024. doi: 10.1088/1126-6708/2002/03/024.
    • Bichl A A, Grimstrup J M, Grosse H, Kraus E, Popp L, Schweda M, Wulkenhaar R. . ‘Noncommutative Lorentz symmetry and the origin of the Seiberg-Witten map.’ European Physical Journal C 24: 491–494. doi: 10.1007/s100520100857.
    • Wulkenhaar R. . Quantum field theories on noncommutative R^4 versus \theta-expanded quantum field theories. [submitted / under review]

    • Bichl A A, Grimstrup J M, Popp L, Schweda M, Grosse H, Wulkenhaar R. . ‘Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map .’ Journal of High Energy Physics 01, No. 06: 013. doi: 10.1088/1126-6708/2001/06/013.
    • Bichl A A, Grimstrup J M, Popp L, Schweda M, Wulkenhaar R. . Deformed QED via Seiberg-Witten map. [submitted / under review]

    • Krajewski T, Wulkenhaar R. . ‘Perturbative quantum gauge fields on the noncommutative torus.’ International Journal of Modern Physics A 15, No. 7: 1011–1029. doi: 10.1142/S0217751X00000495.
    • Wulkenhaar R. . „Slavnov-Taylor identity in noncommutative geometry.“ International Journal of Modern Physics B 14, No. 22-23: 2503–2509. doi: 10.1142/S0217979200002053.
    • Bichl A A, Grimstrup J M, Popp L, Schweda M, Grosse H, Wulkenhaar R. . ‘The superfield formalism applied to the non-commutative Wess-Zumino model.’ Journal of High Energy Physics 00, No. 10: 046. doi: 10.1088/1126-6708/2000/10/046.
    • Grosse H, Krajewski T, Wulkenhaar R. . Renormalization of noncommutative Yang-Mills theories: A simple example. [submitted / under review]

    • Krajewski T, Wulkenhaar R. . ‘On Kreimer's Hopf algebra structure of Feynman graphs.’ European Physical Journal C: Particles and Fields 7, No. 4: 697–708. doi: 10.1007/s100520050439.
    • Wulkenhaar R. . ‘SO(10)-unification in noncommutative geometry revisited.’ International Journal of Modern Physics A 14, No. 4: 559–588. doi: 10.1142/S0217751X99000282.
    • Wulkenhaar R. . ‘Gauge theories with graded differential Lie algebras.’ Journal of Mathematical Physics 40, No. 2: 787–794. doi: 10.1063/1.532685.
    • Wulkenhaar, R. . ‘On Feynman graphs as elements of a Hopf algebra.’ In Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions, edited by Kastler D, Rosso M, Schücker T, 233–242. Nova Science Publishers.
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    • Wulkenhaar R. . ‘Noncommutative geometry with graded differential Lie algebras.’ Journal of Mathematical Physics 38, No. 6: 3358–3390. doi: 10.1063/1.532048.
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    • Wulkenhaar R. . Gyros as geometry of the standard model. [submitted / under review]

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