Remarks
The following data are generated from CRIS. They have shortcomings.
- Research topics are better described here (currently only in German).
- In publications, CRIS does not support arXiv numbers. These can be found in the traditional list of publications. Further informationen can be obtained from INSPIRE and arXiv.
- The list of teaching activities is complete, but useless. Better informationen is given here (in German).
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
- Scientific Assistant, Max-Planck-Institute for Mathematics in the Sciences, Leipzig
- Maître de Conférence invité, Université de Provence, Marseille
- Marie-Curie Fellow, Faculty of Physics, University of Vienna
- DAAD Postdoc Fellow, Centre de Physique Théorique, Marseille
Projects
Selection
- EXC 2044 - B3: Operator algebras & mathematical physics ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - CRC 1442: Geometry: Deformation and Rigidity - D03: Integrability ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/1, D03 - RTG 2149 - Srong and Weak Interactions - from Hadrons to Dark Matter ( – )
Main DFG-Project Hosted at the University of Münster: DFG - Research Training Group | Project Number: GRK 2149/1 - CRC 878 C04 - Mathematical aspects of QFT and condensed matter ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre - CRC 478 E04 - Noncommutative geometry and quantisation of physical interactions ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: INST 211/389-1:3
Complete List
- EXC 2044 - B3: Operator algebras & mathematical physics ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C1: Evolution and asymptotics ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - EXC 2044 - C3: Interacting particle systems and phase transitions ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Cluster of Excellence | Project Number: EXC 2044/1 - RTG 2149: Strong and Weak Interactions - from Hadrons to Dark Matter ( – )
Main DFG-Project Hosted at the University of Münster: DFG - Research Training Group | Project Number: GRK 2149/2-2020; GRK 2149/2-2022 - CRC 1442: Geometry: Deformation and Rigidity - D03: Integrability ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: SFB 1442/1, D03 - RTG 2149 - Srong and Weak Interactions - from Hadrons to Dark Matter ( – )
Main DFG-Project Hosted at the University of Münster: DFG - Research Training Group | Project Number: GRK 2149/1 - CRC 878 C04 - Mathematical aspects of QFT and condensed matter ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre - EU-NCG – Noncommutative Geometry ( – )
EU-Project Hosted outside the University of Münster: EC FP 6 - Marie Curie Actions - Research Training Networks | Project Number: MRTN-CT-2006-031962 - CRC 478 E04 - Noncommutative geometry and quantisation of physical interactions ( – )
Subproject in DFG-Joint Project Hosted at the University of Münster: DFG - Collaborative Research Centre | Project Number: INST 211/389-1:3
- EXC 2044 - B3: Operator algebras & mathematical physics ( – )
Publications
Selection
- . . ‘An algebraic approach to a quartic analogue of the Kontsevich model.’ Mathematical Proceedings 174, No. 3: 471–495. doi: 10.1017/S0305004122000366.
- . . ‘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.
- . . ‘Lambert-W solves the noncommutative \Phi^4-model.’ Communications in Mathematical Physics 374: 1935–1961. doi: 10.1007/s00220-019-03592-4.
- . . Solution of all quartic matrix models arXiv. doi: 10.48550/arXiv.1906.04600. [submitted / under review]
- . . ‘Quantum field theory on noncommutative spaces.’ In Advances in Noncommutative Geometry, edited by , 607–690. Cham: Springer International Publishing. doi: 10.1007/978-3-030-29597-4_11.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . ‘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
- . . ‘Real symmetric Φ^4-matrix model as Calogero-Moser model.’ Letters in Mathematical Physics 114: 25. doi: 10.1007/s11005-024-01772-5.
- . . ‘Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra.’ Journal of Mathematical Physics 64, No. 7: 073505. doi: 10.1063/5.0150975.
- . . A short note on BKP for the Kontsevich matrix model with arbitrary potential arXiv. doi: 10.48550/arXiv.2306.01501. [submitted / under review]
- . . Blobbed topological recursion from extended loop equations arXiv. doi: 10.48550/arXiv.2301.04068. [submitted / under review]
- . . ‘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.
- . . ‘An algebraic approach to a quartic analogue of the Kontsevich model.’ Mathematical Proceedings 174, No. 3: 471–495. doi: 10.1017/S0305004122000366.
- . . ‘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.
- . . ‘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.
- . . ‘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.
- . . Intersection theory of the complex quartic Kontsevich model arXiv. doi: 10.48550/arXiv.2212.01359. [submitted / under review]
- . . ‘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.
- . . ‘Perturbative and geometric analysis of the quartic Kontsevich model.’ Symmetry, Integrability and Geometry: Methods and Applications 17: 085. doi: 10.3842/SIGMA.2021.085.
- . . Blobbed topological recursion of the quartic Kontsevich model II: Genus=0 arXiv. doi: 10.48550/arXiv.2103.13271. [submitted / under review]
- . . ‘Solution of the self-dual \Phi^4 QFT-model on four-dimensional Moyal space.’ Journal of High Energy Physics (JHEP) 01: 081. doi: 10.1007/JHEP01(2020)081.
- . . ‘The Leutwyler-Smilga relation on the lattice.’ Modern Physics Letters A 35, No. 01: 1950346. doi: 10.1142/S0217732319503462.
- . . ‘Lambert-W solves the noncommutative \Phi^4-model.’ Communications in Mathematical Physics 374: 1935–1961. doi: 10.1007/s00220-019-03592-4.
- . . ‘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.
- . . ‘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.
- . . Solution of all quartic matrix models arXiv. doi: 10.48550/arXiv.1906.04600. [submitted / under review]
- . . ‘Quantum field theory on noncommutative spaces.’ In Advances in Noncommutative Geometry, edited by , 607–690. Cham: Springer International Publishing. doi: 10.1007/978-3-030-29597-4_11.
- . . ‘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.
- . . ‘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.
- . . ‘Noncommutative 3-colour scalar quantum field theory model in 2D.’ European Physical Journal C 78: 580. doi: 10.1140/epjc/s10052-018-6042-3.
- . . ‘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.
- . . ‘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.
- . . ‘Exact solution of matricial \Phi^3_2 quantum field theory.’ Nuclear Physics B 925: 319–347. doi: 10.1016/j.nuclphysb.2017.10.010.
- . . The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices arXiv.org. doi: 10.48550/arXiv.1701.07719. [submitted / under review]
- . . ‘Reflection positivity in large-deformation limits of noncommutative field theories.’ Contributed to the Reflection Positivity, Oberwolfach. doi: 10.4171/OWR/2017/55.
- . . ‘Integrability in a 4D QFT model.’ Contributed to the Recent Mathematical Developments in Quantum Field Theory, Oberwolfach. doi: 10.4171/OWR/2016/36.
- . . ‘Construction of a quantum field theory in four dimensions.’ PoS - Proceedings of Science 224: 151. doi: 10.22323/1.224.0151.
- . . ‘A solvable four-dimensional QFT.’ In Quantum Mathematical Physics - A Bridge between Mathematics and Physics, edited by , 153–180. Cham Heidelberg New York Dordrecht London: Springer International Publishing. doi: 10.1007/978-3-319-26902-3_8.
- . . ‘The Moyal sphere.’ Journal of Mathematical Physics 2016, No. 57: 112301. doi: 10.1063/1.4965446.
- . . ‘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.
- . . ‘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.
- . . ‘Towards a construction of a quantum field theory in four dimensions.’ In Mathematical Structures of the Universe, edited by , 227–258. Kraków: Copernicus Center Press.
- . . ‘Noncommutative quantum field theory.’ Fortschritte der Physik 62, No. 9-10: 797–811. doi: 10.1002/prop.201400020.
- . . Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity arXiv. doi: 10.48550/arXiv.1406.7755. [submitted / under review]
- . . ‘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.
- . . ‘Construction of the \Phi^4_4-quantum field theory on noncommutative Moyal space.’ RIMS Kôkyûroku 2014, No. 1904: 67–104.
- . . ‘Spectral geometry of the Moyal plane with harmonic propagation.’ Journal of Noncommutative Geometry 7, No. 4: 939–979. doi: 10.4171/JNCG/140.
- . . ‘Construction and properties of noncommutative quantum fields.’ In XVIIth International Congress on Mathematical Physics, edited by , 643–650. Singapore: World Scientific Publishing. doi: 10.1142/9789814449243_0066.
- . . Solvable limits of a 4D noncommutative QFT arXiv. doi: 10.48550/arXiv.1306.2816. [submitted / under review]
- . . ‘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 , 153–163. Providence, RI: American Mathematical Society. doi: 10.1090/pspum/087/01442.
- . . ‘A numerical approach to harmonic non-commutative spectral field theory.’ International Journal of Modern Physics A 27, No. 14: 1250075. doi: 10.1142/S0217751X12500753.
- . . ‘Renormalization of a noncommutative field theory.’ International Journal of Modern Physics A 27, No. 12: 1250067. doi: 10.1142/S0217751X12500674.
- . . ‘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.
- . . ‘Renormalization of a noncommutative field theory.’ International Journal of Modern Physics: Conference Series 13: 108–117. doi: 10.1142/S2010194512006770.
- . . ‘Renormalizable noncommutative quantum field theory.’ Journal of Physics: Conference Series 343: 012043. doi: 10.1088/1742-6596/343/1/012043.
- . . ‘Renormalisation of the Grosse-Wulkenhaar model.’ PoS - Proceedings of Science QGQGS, No. 2011: 011.
- . . ‘Renormalizable noncommutative quantum field theory.’ General Relativity and Gravitation 43: 2491–2498. doi: 10.1007/s10714-010-1065-6.
- . . ‘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.
- . . ‘Non-compact spectral triples with finite volume.’ In Quanta of Maths, edited by , 617–648. Providence, RI: American Mathematical Society.
- . . ‘Progress in solving a noncommutative QFT in four dimensions.’ Contributed to the Noncommutative Geometry, Oberwolfach. doi: 10.4171/OWR/2009/41.
- . . Progress in solving a noncommutative quantum field theory in four dimensions arXiv. doi: 10.48550/arXiv.0909.1389. [submitted / under review]
- . . ‘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.
- . . ‘Renormalization of noncommutative quantum field theory.’ In An invitation to noncommutative geometry, edited by , 129–168. Singapore: World Scientific Publishing. doi: 10.1142/9789812814333_0002.
- . . ‘Quantum field theory on projective modules.’ Journal of Noncommutative Geometry 1, No. 4: 431–496. doi: 10.4171/JNCG/13.
- . . ‘Noncommutative induced gauge theory.’ European Physical Journal C: Particles and Fields 51, No. 4: 977–987. doi: 10.1140/epjc/s10052-007-0335-2.
- . . ‘Noncommutative QFT and renormalization.’ In Quantum Gravity - Mathematical Models and Experimental Bounds, edited by , 315–326. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-7643-7978-0_16.
- . . ‘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.
- . . ‘Renormalisation scalar quantum field theory on 4D-Moyal plane.’ Contributed to the The Rigorous Renormalization Group, Oberwolfach. doi: 10.4171/OWR/2006/17.
- . . ‘Noncommutative QFT and renormalization.’ Fortschritte der Physik 54, No. 2-3: 116–123. doi: 10.1002/prop.200510260.
- . . ‘Noncommutative QFT and renormalization.’ Bulgarian Journal of Physics 33, No. s1: 215–225.
- . . ‘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.
- . . ‘Field theories on deformed spaces.’ Journal of Geometry and Physics 56, No. 1: 108–141. doi: 10.1016/j.geomphys.2005.04.019.
- . . ‘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.
- . . ‘Euclidean quantum field theory on commutative and noncommutative spaces.’ In Geometric and Topological Methods for Quantum Field Theory, edited by , 59––100. Berlin: Springer VDI Verlag. doi: 10.1007/11374060_2.
- . . ‘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.
- . . ‘Renormalisation of scalar quantum field theory on noncommutative R^4 .’ Fortschritte der Physik 53, No. 5-6: 634––639. doi: 10.1002/prop.200410231.
- . . ‘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.
- . . ‘Renormalisation of noncommutative scalar field theories.’ In Lie Theory and its Applications in Physics V, edited by , 109–123. World Scientific Publishing. doi: 10.1142/9789812702562_0006.
- . . ‘Renormalisation of noncommutative quantum field theories.’ Czechoslovak Journal of Physics 54, No. 11: 1305–1311. doi: 10.1007/s10582-004-9793-z.
- . . ‘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.
- . . ‘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.
- . . ‘IR singularities in noncommutative perturbative dynamics?’ Europhysics Letters 67, No. 2: 186–190. doi: 10.1209/epl/i2003-10285-9.
- . . ‘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.
- . ‘ Renormalisation of noncommutative \phi^4-theory to all orders.’ contributed to the Nichtkommutative Geometrie, Oberwolfach, . doi: 10.4171/OWR/2004/45.
- . . ‘Renormalisation group approach to noncommutative quantum field theory.’ In Particle Physics and the Universe, edited by , 197–208. Springer VDI Verlag. doi: 10.1007/3-540-26798-0_19.
- . . ‘Renormalisation of \phi^4-theory on noncommutative R^2 in the matrix base .’ Journal of High Energy Physics (JHEP) 03, No. 12: 019. doi: 10.1088/1126-6708/2003/12/019.
- . . ‘Seiberg-Witten map for noncommutative super Yang-Mills theory.’ International Journal of Modern Physics A 18, No. 19: 3325–3334. doi: 10.1142/S0217751X03015246.
- . . ‘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.
- . . ‘Regularisation and renormalisation of quantum field theories on noncommutative spaces.’ In Modern Mathematical Physics, edited by , 29–46.: Belgrade Institute of Physics.
- . . ‘Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry.’ Journal of Mathematical Physics 43, No. 1: 182–204. doi: 10.1063/1.1418012.
- . . ‘Introduction to Hopf algebras in renormalization and noncommutative geometry.’ In Noncommutative geometry and the standard model of elementary particle physics, edited by , 313–324. Berlin: Springer VDI Verlag. doi: 10.1007/3-540-46082-9_17.
- . . ‘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.
- . . ‘The energy-momentum tensor on noncommutative spaces -- some pedagogical comments .’ Ukrainian Journal of Physics 47, No. 3: 219–225.
- . . ‘Noncommutative spin-1/2 representations.’ European Physical Journal C: Particles and Fields 24, No. 3: 491––494. doi: 10.1007/s10052-002-0938-6.
- . . ‘Perturbative analysis of the Seiberg-Witten map.’ International Journal of Modern Physics A 17, No. 16: 2219–2231. doi: 10.1142/S0217751X02010649.
- . . ‘Non-renormalizability of \theta-expanded non-commutative QED.’ Journal of High Energy Physics (JHEP) 02, No. 03: 024. doi: 10.1088/1126-6708/2002/03/024.
- . . ‘Noncommutative Lorentz symmetry and the origin of the Seiberg-Witten map.’ European Physical Journal C 24: 491–494. doi: 10.1007/s100520100857.
- . . Quantum field theories on noncommutative R^4 versus \theta-expanded quantum field theories. [submitted / under review]
- . . ‘Renormalization of the noncommutative photon self-energy to all orders via Seiberg-Witten map .’ Journal of High Energy Physics (JHEP) 01, No. 06: 013. doi: 10.1088/1126-6708/2001/06/013.
- . . Deformed QED via Seiberg-Witten map. [submitted / under review]
- . . ‘Perturbative quantum gauge fields on the noncommutative torus.’ International Journal of Modern Physics A 15, No. 7: 1011–1029. doi: 10.1142/S0217751X00000495.
- . . „Slavnov-Taylor identity in noncommutative geometry.“ International Journal of Modern Physics B 14, No. 22-23: 2503–2509. doi: 10.1142/S0217979200002053.
- . . ‘The superfield formalism applied to the non-commutative Wess-Zumino model.’ Journal of High Energy Physics (JHEP) 00, No. 10: 046. doi: 10.1088/1126-6708/2000/10/046.
- . . Renormalization of noncommutative Yang-Mills theories: A simple example. [submitted / under review]
- . . ‘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.
- . . ‘SO(10)-unification in noncommutative geometry revisited.’ International Journal of Modern Physics A 14, No. 4: 559–588. doi: 10.1142/S0217751X99000282.
- . . ‘Gauge theories with graded differential Lie algebras.’ Journal of Mathematical Physics 40, No. 2: 787–794. doi: 10.1063/1.532685.
- . . ‘On Feynman graphs as elements of a Hopf algebra.’ In Quantum Groups, Noncommutative Geometry and Fundamental Physical Interactions, edited by , 233–242. Nova Science Publishers.
- . . On the Connes-Moscovici Hopf algebra associated to the diffeomorphisms of a manifold. [submitted / under review]
- . . ‘Graded differential Lie algebras and SU(5) x U(1)-grand unification .’ International Journal of Modern Physics A 13, No. 15: 2627–2692. doi: 10.1142/S0217751X98001359.
- . . ‘Graded differential Lie algebras and model building.’ Journal of Geometry and Physics 25, No. 3-4: 305–325. doi: 10.1016/S0393-0440(97)00029-6.
- . . ‘Gauge field theories in terms of graded differential Lie algebras.’ In Lie Theory and its Applications in Physics II, edited by , 310–321. World Scientific Publishing. doi: 10.1142/3852.
- . . ‘Noncommutative geometry with graded differential Lie algebras.’ Journal of Mathematical Physics 38, No. 6: 3358–3390. doi: 10.1063/1.532048.
- . . ‘The standard model within non-associative geometry.’ Physics Letters B 390, No. 1-4: 119–127. doi: 10.1016/S0370-2693(96)01336-6.
- . . ‘Yang-Mills-Higgs models arising from L-cycles.’ In GROUP 21, edited by , 597–601. World Scientific Publishing. doi: 10.1142/3473.
- . . Gyros as geometry of the standard model. [submitted / under review]
- . . ‘Graded Lie algebras with derivation and model building.’ In Lie Theory and its Applications in Physics, edited by , 149–158. World Scientific Publishing. doi: 10.1142/3301.
- . . ‘On certain graded Lie algebras arising in noncommutative geometry .’ Acta Physica Polonica Series B 27, No. 10: 2755–2762.
- . . ‘On the structure of a differential algebra used by Connes and Lott.’ Reports on Mathematical Physics 38, No. 1: 45–66. doi: 10.1016/0034-4877(96)87677-4.
- . . ‘On a certain construction of graded Lie algebras with derivation.’ Journal of Geometry and Physics 20, No. 2-3: 107–141. doi: 10.1016/0393-0440(95)00048-8.
- . . ‘Deriving the standard model from the simplest two-point K-cycle.’ Journal of Mathematical Physics 37, No. 8: 3797–3814. doi: 10.1063/1.531602.
Supervised Doctoral Studies
Harengel, Katharina The combinatorial structure of correlation functions in the quartic Kontsevich model and its connections to freeness in free probability Jost, Finn Bjarne Topological recursion of the quartic Kontsevich model Branahl, Johannes The Recursive Structure of the Quartic Kontsevich Model Pascalie, Romain Random tensors and the Sachdev-Ye-Kitaev model Hock, Alexander Matrix Field Theory Gerber, Henning Non-perturbative investigations of light bound states of N=1 supersymmetric Yang-Mills theory de Jong, Jins Partition function methods for the quartic scalar quantum field theory on the Moyal plane Perez Sanchez, Carlos Ignacio The Ward-Takahashi identity and the Schwinger-Dyson equations for colored tensor models Pfante, Oliver Noncommutative Chern-Simons theory Spisso, Bernardino A numerical approach to harmonic non-commutative spectral field theory Marcillaud de Goursac, Axel Noncommutative Geometry, Gauge Theory and Renormalization Schmidt, René Arithmetic gravity and Yang-Mills theory: An approach to adelic physics via algebraic spaces Talks
- Wulkenhaar, Raimar (): ‘Quantum fields on noncommutative geometries’. Workshop on Operator Algebras and Applications: Non-Commutative Geometry (Fields Institute), Toronto, .
- Wulkenhaar, Raimar (): ‘Matrix models and topological recursion’. Kolloquium Mathematische Physik, Universität Bielefeld (Universität Bielefeld), Bielefeld, .
- Wulkenhaar, Raimar (): ‘Blobbed topological recursion of quartic matrix models’. Invitation to Recursion, Resurgence and Combinatorics (Okinawa Institute of Science and Technology), Okinawa, .
- Wulkenhaar, Raimar (): ‘Blobbed topological recursion of the \lambda \Phi^4 matrix model’. Quantum Gravity and Random Geometry (Institut Henri Poincaré), Paris, .
- Wulkenhaar, Raimar (): ‘The Euclidean λφ^4_4-model on noncommutative geometries: a status report’. Energy conditions in quantum field theory (Institut für Theoretische Physik, Universität Leipzig), Leipzig, .
- Wulkenhaar; Raimar (): ‘How topological recursion organises quantum fields on noncommutative geometries (3 lectures)’. Fields Institute Workshop on Noncommutative Geometry, Free Probability Theory and Random Matrix Theory (University of Western Ontario), London (Ontario), .
- Wulkenhaar, Raimar (): ‘Solution of the λΦ^4-matrix model’. Random Geometry in Heidelberg (Universität Heidelberg), Heidelberg, .
- Wulkenhaar, Raimar (): ‘From scalar fields on noncommutativegeometries to blobbed topological recursion’. Emmy-Noether Seminar (Institut für Theoretische Physik, Universität Leipzig), Universität Leipzig, Deutschland, .
- Wulkenhaar, Raimar (): ‘On ‘Topological recursion, discrete surfaces and cohomological field theories’ by Elba Garcia-Failde’. Higher Structures Emerging from Renormalisation (Erwin-Schrödinger-Institut, Vienna, Austria), Erwin-Schrödinger-Institut, Vienna, Austria, .
- Wulkenhaar, Raimar (): ‘From scalar fields on noncommutative geometries to blobbed topological recursion’. Workshop on Quantum Geometry, Field Theory and Gravity (Corfu Summer Institute), Corfu, Greece, .
- Wulkenhaar, Raimar (): ‘From noncommutative field theory towards topological recurrence’. Noncommutative Geometry and Physics (Noncommutative Geometry and Physics), (remotely), .
- Wulkenhaar, Raimar (): ‘Topological recursion of scalar fields in noncommutative geometry’. The Noncommutative Geometry Seminar (Global NCG Seminar), (remotely), .
- Wulkenhaar, Raimar (): ‘Blobbed topological recursion of the quartic analogue of the Kontsevich model’. Research seminar "Structure of Local Quantum Field Theories", Humboldt-Universität zu Berlin (Humboldt-Universität), Berlin, Deutschland, .
- Wulkenhaar, Raimar (): ‘Solvable Dyson-Schwinger equations’. Algebraic Structures in Perturbative Quantum Field Theory (IHÉS), IHÉS, Bures-sur-Yvette, France (remote workshop), .
- Wulkenhaar, Raimar (): ‘Blobbed topological recursion of the quartic analogue of the Kontsevich model’. ESI Workshop "Higher Structures Emerging from Renormalisation" (Erwin Schrödinger Institute), Erwin Schrödinger Institute, Vienna, Austria (remote workshop), .
- Wulkenhaar, Raimar (): ‘The complete solution of the quartic analogue of the Kontsevich model’. Mathematical Physics Seminar (Harbin Institute of Technology), Harbin, China (remote talk), .
- Wulkenhaar, Raimar (): ‘The complete solution of the quartic analogue of the Kontsevich model’. Séminaire de physique mathématique (Institut Camille Jordan, Université de Lyon), Lyon, France (remote talk), .
- Wulkenhaar, Raimar (): ‘Towards integrability of a quartic analogue of the Kontsevich model’. Quantum Field Theory Seminar, Mathematical Institute, University of Oxford, Oxford, United Kingdom, .
- Wulkenhaar, Raimar (): ‘Solution of all quartic matrix models’. Mathematics of interacting QFT models, York, United Kingdom, .
- Wulkenhaar, Raimar (): ‘Matrix models’. Colloquium of the Department of Mathematics (Fachrichtung Mathematik, Universität des Saarlandes), Saarbrücken, Deutschland, .
- Wulkenhaar, Raimar (): ‘Solvable quantum field theories on noncommutative geometry’. Theoretical Physics and Mathematics (TPM) lecture (CP3-Origins), Odense, Denmark, .
- Wulkenhaar, Raimar (): ‘Lambert-W solves the noncommutative \phi^4-model’. Non-commutative Geometry, Index Theory and Mathematical Physics (Mathematisches Forschungsinstitut Oferwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘Integrability in QFT-models on noncommutative geometry’. Structures in local quantum field theory (École de Physique des Houches), Les Houches, France, .
- Wulkenhaar, Raimar (): ‘From NCQFT studied with Manfred to integrable QFT models’. Manfred Schweda Memorial Meeting (Technische Universität Wien), Wien, Österreich, .
- Wulkenhaar, Raimar (): ‘Reflection positivity in large-deformation limits of noncommutative field theories’. Reflection Positivity (Mathematisches Forschungsinstitut Oferwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘Matricial quantum field theory’. Field Theories and Higher Structures in Mathematics and Physics (Casa Matemática Oaxaca), Oaxaca, Mexico, .
- Wulkenhaar, Raimar (): ‘Matricial quantum field theory: renormalisation, integrability & positivity’. Wolfhart Zimmermann Memorial Symposium (Max-Planck-Institut für Physik), München, Deutschland, .
- Wulkenhaar, Raimar (): ‘Matricial.quantum field theory: Integrability. Positivity?’ Noncommutative Geometry: Index Theory and its Ramifications in Geometry, Topology, and Physics (Shanghai Center for Mathematical Sciences), Shanghai, China, .
- Wulkenhaar, Raimar (): ‘Exact solution of quantum field theory toy models’. Seminar Mathematische Physik (Fakultät für Physik, Universität Wien), Wien, Österreich, .
- Wulkenhaar, Raimar (): ‘Integrability in a 4D QFT model’. Recent Mathematical Developments in Quantum Field Theory (Mathematisches Forschungsinstitut Oferwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘A solvable quantum field theory in 4 dimensions’. Colloquium in Honour of Gerd Rudolph (Institut für Theoretische Physik, Universität Leipzig), Leipzig, Deutschland, .
- Wulkenhaar, Raimar (): ‘A solvable quantum field theory in 4 dimensions’. Séminaire de physique mathématique, Institut Camille Jordan (Université Lyon 1, Institut Camille Jordan), Lyon, France, .
- Wulkenhaar, Raimar (): ‘Mathematical Physics’. Retreat des GRK 2149 (GRK 2149 "Strong and Weak Interactions - from Hadrons to Dark Matter"), Telgte, Deutschland, .
- Wulkenhaar, Raimar (): ‘A solvable quantum field theory in 4 dimensions’. Workshop on Noncommutative Field Theory and Gravity (Corfu Summer Institute), Corfu, Greece, .
- Wulkenhaar, Raimar (): ‘A solvable quantum field theory in 4 dimensions’. International Conference in Number Theory and Physics (Instituto Nacional de Matemática Pura e Aplicada), Rio de Janeiro, Brazil, .
- Wulkenhaar, Raimar (): ‘A solvable quantum field theory in 4 dimensions’. Seminar Humboldt-Universität (Institut für Mathematik, Humboldt-Universität zu Berlin), Berlin, Deutschland, .
- Wulkenhaar, Raimar (): ‘Exact solution of a four-dimensional field theory’. Geometric and Algebraic Methods in Mathematical Physics (Fakultät für Mathematik, TU Dortmund), Dortmund, Deutschland, .
- Wulkenhaar, Raimar (): ‘A non-trivial four-dimensional QFT. Part II’. Quantum Mathematical Physics - A Bridge between Mathematics and Physics (University of Regensburg, Johannes Kepler Institute for Mathematics), Regensburg, Deutschland, .
- Wulkenhaar, Raimar (): ‘Exact solution of a four-dimensional field theory’. Hausdorff Trimester Program Non-commutative Geometry and its Applications (Hausdorff Research Institute for Mathematics), Bonn, Deutschland, .
- Wulkenhaar, Raimar (): ‘Towards construction of a Wightman QFT in four dimensions’. Quantum Gravity Seminar, Perimeter Institute (Perimeter Institute), Waterloo, Canada, .
- Wulkenhaar, Raimar (): ‘Construction of a quantum field theory in four dimensions’. Frontiers of Fundamental Physics 14 (Aix-Marseille Université), Marseille, France, .
- Wulkenhaar, Raimar (): ‘Construction of a quantum field theory in four dimensions’. Quantized geometry and physics (Courant Research Centre "Higher Order Structures in Mathematics", Göttingen), Bayrischzell, Deutschland, .
- Wulkenhaar, Raimar (): ‘Exact solution of the quartic matrix model’. Quantum Gravity in Paris (Max Planck Institute for Gravitational Physics, Potsdam), Orsay, France, .
- Wulkenhaar, Raimar (): ‘Schwinger functions and reflection positivity’. Lecture Series "A solvable (noncommutative) QFT in 4 dimensions" (Courant Research Centre "Higher Order Structures in Mathematics", Göttingen), Göttingen, Deutschland, .
- Wulkenhaar, Raimar (): ‘The Moyal space-\phi^4_4-QFT as a fixed point problem’. Lecture Series "A solvable (noncommutative) QFT in 4 dimensions" (Courant Research Centre "Higher Order Structures in Mathematics", Göttingen), Göttingen, Deutschland, .
- Wulkenhaar, Raimar (): ‘Solution of the quartic matrix model’. Lecture Series "A solvable (noncommutative) QFT in 4 dimensions" (Courant Research Centre "Higher Order Structures in Mathematics", Göttingen), Göttingen, Deutschland, .
- Wulkenhaar, Raimar (): ‘Construction of a 4D quantum field theory’. Lecture Series "A solvable (noncommutative) QFT in 4 dimensions" (Courant Research Centre "Higher Order Structures in Mathematics", Göttingen), Göttingen, Deutschland, .
- Wulkenhaar, Raimar (): ‘Construction of a 4D (noncommutative) quantum field theory’. Oberseminar Stochastik (AG Stochastik, Bergische Universität Wuppertal), Wuppertal, Deutschland, .
- Wulkenhaar, Raimar (): ‘Non-trivial \Phi^4_4 on Moyal space I.+II.’ Applications of Renormalization Group Methods in Mathematical Sciences (Research Institute for Mathematical Sciences, Kyoto University), Kyoto, Japan, .
- Wulkenhaar, Raimar (): ‘Noncommutative Geometry I.+II.’ RIMS-Seminar, Kyoto University (Research Institute for Mathematical Sciences, Kyoto University), Kyoto, Japan, .
- Wulkenhaar, Raimar (): ‘Exact solution of the quartic matrix model and application to 4D noncommutative QFT’. Séminaire Mathématique, Laboratoire de Physique Théorique (Laboratoire de Physique Théorique, Université Paris Sud), Orsay, France, .
- Wulkenhaar, Raimar (): ‘Exact solution of the quartic matrix model and application to 4D noncommutative QFT’. Noncommutative Geometry Seminar (Mathematical Institute of the Polish Academy of Sciences (IMPAN)), Warszawa, Poland, .
- Wulkenhaar, Raimar (): ‘Solvable quantum field theory models’. Mathematical Colloquium, Radboud Universiteit (Faculty of Science Institute for Mathematics, Astrophysics and Particle Physics, Radboud Universiteit), Nijmegen, The Netherlands, .
- Wulkenhaar, Raimar (): ‘Exact solution of a non-local four-dimensional quantum field theory’. 31st LQP Workshop "Foundations and Constructive Aspects of QFT" (Max Planck Institute for Mathematics in the Sciences), Leipzig, Deutschland, .
- Wulkenhaar, Raimar (): ‘Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory’. ESI Programme on “K-Theory and Quantum Fields” (Erwin Schrödinger Institute, Wien), Wien, Österreich, .
- Wulkenhaar, Raimar (): ‘Self-dual noncommutative \phi^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory’. NCGOA Spring Institute on Conformal Field Theory and von Neumann Algebras (Department of Mathematics, Vanderbilt University), Nashville, USA, .
- Wulkenhaar, Raimar (): ‘Progress in solving noncommutative \phi^4-theory in four dimensions’. Planckland - Quantum Geometry and Matter (SISSA), Trieste, Italia, .
- Wulkenhaar, Raimar (): ‘Ward identities in matrix models arising from noncommutative geometry’. Quantum Theory and Gravitation (Institute for Theoretical Physics, ETH Zürich), Zürich, Schweiz, .
- Wulkenhaar, Raimar (): ‘The two-point function of noncommutative \phi^4_4-theory’. Kolloquium des GRK1463 (GRK 1463 "Analysis, Geometry and String Theory"), Hannover, Deutschland, .
- Wulkenhaar, Raimar (): ‘The two-point function of noncommutative \phi^4_4-theory’. Noncommutativity and Physics: Spacetime Quantum Geometry (Quantum Geometry and Quantum Gravity Network of the ESF), Bayrischzell, Deutschland, .
- Wulkenhaar, Raimar (): ‘QFT on NCG’. Noncommutative Geometry and Loop Quantum Gravity: Loops, Algebras and Spectral Triples (Mathematisches Forschungsinstitut Oberwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘Noncommutative spacetime’. The Physics of the Spectral Action, IHES (IHES), Bures-sur-Yvette, France, .
- Wulkenhaar, Raimar (): ‘Non-compact spectral triples’. EU mid term review and conference "Quantum Spaces and Non-commutative Geometry" (Department of Mathematical Sciences, University of Copenhagen), Copenhagen, Denmark, .
- Wulkenhaar, Raimar (): ‘The standard model in NCG I.+II.’ DPG - Physics School 2009: Mathematical Physics (Physikzentrum Bad Honnef), Bad Honnef, Deutschland, .
- Wulkenhaar, Raimar (): ‘Noncommutative Geometry I.-V.’ DPG - Physics School 2009: Mathematical Physics (Physikzentrum Bad Honnef), Bad Honnef, Deutschland, .
- Wulkenhaar, Raimar (): ‘Progress in solving a noncommutative quantum field theory in four dimensions’. Noncommutative Geometry (Mathematisches Forschungsinstitut Oberwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘The matrix base of the Moyal space and interesting results obtained with it’. 2nd School & Conference on Noncommutative Geometry (Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran), Tehran, Iran, .
- Wulkenhaar, Raimar (): ‘An overview of quantum field theory I.+II.’ 2nd School & Conference on Noncommutative Geometry (Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran), Tehran, Iran, .
- Wulkenhaar, Raimar (): ‘Non-compact spectral triples with finite volume’. ESI Program on Number Theory and Physics (Erwin Schrödinger Institute, Wien), Wien, Österreich, .
- Wulkenhaar, Raimar (): ‘Noncommutative Quantum Field Theory’. Theoriekolloquium des Instituts für Physik, Johannes Gutenberg-Universität (Institut für Physik, Johannes Gutenberg-Universität), Mainz, Deutschland, .
- Wulkenhaar, Raimar (): ‘Non-compact spectral triples with finite volume’. QFT Seminar, Humboldt-Universität (Quantum Field and String Theory Group, Humboldt-Universität zu Berlin), Berlin, Deutschland, .
- Wulkenhaar, Raimar (): ‘Non-compact spectral triples with finite volume’. Seminar des II. Instituts für Theoretische Physik (II. Institut für Theoretische Physik, Universität Hamburg), Hamburg, Deutschland, .
- Wulkenhaar, Raimar (): ‘Non-compact spectral triples with finite volume’. Quantum Spacetime and Noncommutative Geometry (Math Department, "La Sapienza" University, Roma), Roma, Italia, .
- Wulkenhaar, Raimar (): ‘A spectral triple for harmonic oscillator Moyal space’. Workshop on Noncommutative Geometry, Hausdorff Trimester Program "Geometry and Physics" (Hausdorff Research Institute for Mathematics), Bonn, Deutschland, .
- Wulkenhaar, Raimar (): ‘A spectral triple for harmonic oscillator Moyal space’. Noncommutative Geometry Workshop, Fields Institute (Fields Institute, Toronto), Toronto, Canda, .
- Wulkenhaar, Raimar (): ‘A spectral triple for harmonic oscillator Moyal space’. Kolloquium der Mathematischen Gesellschaft (Mathematisches Institut, Georg-AugustUniversität Göttingen), Göttingen, Deutschland, .
- Wulkenhaar, Raimar (): ‘A spectral triple for Moyal space with harmonic oscillator potential’. Mini-workshop on Fuzzy Physics and Random Matrices (Dublin Institute for Advanced Studies), Dublin, Ireland, .
- Wulkenhaar, Raimar (): ‘Renormalisation of \phi^4_4-theory on Moyal space with oscillator potential’. Mini-workshop on Fuzzy Physics and Random Matrices (Dublin Institute for Advanced Studies), Dublin, Ireland, .
- Wulkenhaar, Raimar (): ‘A spectral triple for Moyal space with harmonic oscillator potential’. ESI Workshop "Noncommutative Quantum Field Theory" (Erwin Schrödinger Institute, Wien; ESF programme Quantum Geometry and Quantum Gravity), Wien, Österreich, .
- Wulkenhaar, Raimar (): ‘From the harmonic oscillator as a spectral triple to the vacuum of noncommutative gauge theory’. Workshop on Noncommutative Manifolds II (SISSA), Trieste, Italia, .
- Wulkenhaar, Raimar (): ‘The harmonic oscillator, its noncommutative dimension and the vacuum of noncommutative gauge theory’. Noncommutative Geometry (Mathematisches Forschungsinstitut Oberwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘Euclidean quantum field theory on noncommutative space’. Seminar des II. Instituts für Theoretische Physik (II. Institut für Theoretische Physik, Universität Hamburg), Hamburg, Deutschland, .
- Wulkenhaar, Raimar (): ‘Quantum field theory on projective modules’. Bayrischzell Workshop 2007 on noncommutativity and physics (DFG priority programme SPP 1096 "String Theory"), Bayrischzell, Deutschland, .
- Wulkenhaar, Raimar (): ‘The matrix base of the Moyal space and interesting results obtained with it’. Non Commutative Geometry and Physics (Laboratoire de Physique Théorique, Université Paris Sud), Orsay, France, .
- Wulkenhaar, Raimar (): ‘Quantum field theory on projective modules’. Noncommutative Spacetime Geometries (Facoltà di Scienze Matematiche Fisiche e Naturali, Università degli studi del Piemonte Orientale), Alessandria, Italia, .
- Wulkenhaar, Raimar (): ‘Renormalisation of quantum field theories on noncommutative geometries’. MPIM-workshop "Renormalization" (Max Planck Institute for Mathematics), Bonn, Deutschland, .
- Wulkenhaar, Raimar (): ‘Renormalisation of quantum field theories on noncommutative geometries’. Noncommutative Geometry and Physics: Fundamental Structure of Space and Time (Isaac Newton Institute for Mathematical Sciences), Cambridge, United Kingdom, .
- Wulkenhaar, Raimar (): ‘Renormalisation of scalar quantum field theory on 4D-Moyal plane’. The Rigorous Renormalization Group (Mathematisches Forschungsinstitut Oberwolfach), Oberwolfach, Deutschland, .
- Wulkenhaar, Raimar (): ‘Renormalisation of scalar quantum field theory on 4D-Moyal plane’. Seminar, Department of Mathematical Sciences (Department of Mathematical Sciences, University of Copenhagen), Copenhagen, Denmark, .
- Wulkenhaar, Raimar (): ‘Renormalisation’. International Conference on Operator Algebras and their connections to Mathematical Physics (Laboratoire de Mathématiques et Informatique et Sciences de l'ingénieur de Settat (LMISIS), University Hassan I, Morocco), Settat, Morocco, .
Other writings
Renormalisation of noncommutative φ44-theory to all orders
Habilitation thesis in Theoretical Physics, submitted to the Faculty of Physics, Vienna University of Technology, July 2004
Non-Associative Geometry - Unified Models Based on L-cycles
Doctoral thesis (for academic degree Dr. rer. nat.), submitted to the Faculty of Physics and Earth Sciences, Leipzig University, 3 November 1997