Publications
- Juliano, L, and Thürigen, J. . “New Fixed Points from Melonic Interactions.” Physics Letters B, № 860: 139218. doi: 10.1016/j.physletb.2024.139218.
- Hock, Alexander, Shadrin, Sergey, and Wulkenhaar, Raimar. . “Symmetry of meromorphic differentials produced by involution identity, and relation to integer partitions.” arXiv doi: 10.48550/arXiv.2501.00082.
- Hock, Alexander, Wulkenhaar, Raimar, and Dołega, Maciej (appendix). Forthcoming. “Blobbed topological recursion of the quartic Kontsevich model II: Genus=0.” Annales de l’Institut Henri Poincaré D: Combinatorics, Physics and their Interactions, № online first doi: 10.4171/AIHPD/198.
- Borot, Gaëtan, and Wulkenhaar, Raimar. . “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. . “Real symmetric Φ^4-matrix model as Calogero-Moser model.” Letters in Mathematical Physics, № 114 25. doi: 10.1007/s11005-024-01772-5.
- Ben Geloun, J, Pithis, A, and Thürigen, J. . “QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization.” Journal of Mathematical Physics, № 65: 032302. doi: 10.1063/5.0158724.
- Hock, A, and Thürigen, J. . “Combinatorial Dyson-Schwinger Equations of Quartic Matrix Field Theory.” arXiv
- Grosse, Harald, Kanomata, Naoyuki, Sako, Akifumi, and Wulkenhaar, Raimar. . “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.
- Melong, Fridolin, and Wulkenhaar, Raimar. . “Generalized Heisenberg-Virasoro algebra and matrix models from quantum algebra.” Journal of Mathematical Physics, № 64 (7) 073505. doi: 10.1063/5.0150975.
- Marchetti, L, Oriti, D, Pithis, A, and Thürigen, J. . “Mean-Field Phase Transitions in TGFT Quantum Gravity.” Physical Review Letters, № 130: 141501. doi: 10.1103/PhysRevLett.130.141501.
- Marchetti, L, Oriti, D, Pithis, A, and Thürigen, J. . “Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models.” Journal of High Energy Physics (JHEP), № 02: 074. doi: 10.1007/JHEP02(2023)074.
- Jercher, A, Steinhaus, S, and Thürigen, J. . “Curvature effects in the spectral dimension of spin foams.” Physical Review D (PRD), № 108: 066011. doi: 10.1103/PhysRevD.108.066011.
- Hock, Alexander, and Wulkenhaar, Raimar. . “Blobbed topological recursion from extended loop equations.” arXiv doi: 10.48550/arXiv.2301.04068.
- Grosse, Harald, Hock, Alexander, and 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, and Wulkenhaar, Raimar. . “An algebraic approach to a quartic analogue of the Kontsevich model.” Mathematical Proceedings, № 174 (3): 471–495. doi: 10.1017/S0305004122000366.
- Branahl, Johannes, Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. . “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.
- Brunekreef, J, Lionni, L, and Thürigen, J. . “One-matrix differential reformulation of two-matrix models.” Reviews in Mathematical Physics, № 34 (08): 2250026. doi: 10.1142/S0129055X2250026X.
- Branahl, Johannes, Hock, Alexander, and 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, and 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 (1): 47–72. doi: 10.4171/AIHPD/113.
- Kohl, Finn Bjarne, and Wulkenhaar, Raimar. . “Intersection theory of the complex quartic Kontsevich model.” arXiv doi: 10.48550/arXiv.2212.01359.
- Pascalie, Romain, Pérez-Sánchez, Carlos Ignacio, and 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 (3): 377–458. doi: 10.4171/AIHPD/107.
- Branahl, Johannes, Hock, Alexander, and 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.
- Pithis, AG, and Thürigen, J. . “(No) phase transition in tensorial group field theory.” Physics Letters B, № 816: 136215. doi: 10.1016/j.physletb.2021.136215.
- Thürigen, J. . “Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme.” Symmetry, Integrability and Geometry: Methods and Applications, № 17: 094. doi: 10.3842/SIGMA.2021.094.
- Thürigen, J. . “Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs.” Math. Phys. Anal. Geom., № 24 (2): 19. doi: 10.1007/s11040-021-09390-6.
- Marchetti, L, Oriti, D, Pithis, A, and Thürigen, J. . “Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom.” JHEP, № 12 (2021): 201. doi: 10.1007/JHEP12(2021)201.
- Münster, Gernot, and Wulkenhaar, Raimar. . “The Leutwyler-Smilga relation on the lattice.” Modern Physics Letters A, № 35 (01): 1950346. doi: 10.1142/S0217732319503462.
- Thürigen, J. . “Functional renormalization group in TGFT - the cyclic-melonic potential approximation.” contribution to the Quantum Spacetime and the Renormalization Group 2020, Odense, Dänemark
- Pithis, AG, and Thürigen, J. . “Phase transitions in TGFT: Functional renormalization group in the cyclic-melonic potential approximation and equivalence to O(N) models.” JHEP, № 12 (2020): 159. doi: 10.1007/JHEP12(2020)159.
- Hock, Alexander. . “Matrix Field Theory.” Dissertation thesis, Universität Münster.
- Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. . “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.
- Panzer, Erik, and Wulkenhaar, Raimar. . “Lambert-W solves the noncommutative ϕ4-model.” Communications in Mathematical Physics, № 374: 1935–1961. doi: 10.1007/s00220-019-03592-4.
- de Jong, Jins, and 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 (8) 083504. doi: 10.1063/1.5063293.
- Pascalie, Romain, Pérez-Sánchez, Carlos Ignacio, Tanasa, Adrian, and Wulkenhaar, Raimar. . “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.
- Grosse, Harald, Hock, Alexander, and Wulkenhaar, Raimar. . “Solution of all quartic matrix models.” arXiv doi: 10.48550/arXiv.1906.04600.
- Thürigen, Johannes. . “Ansätze zur Quantengravitation - fundamentale Physik am Rande des Begriffs der Naturwissenschaft.” Briefe zur Interdisziplinarität, № 23: 26–36.
- Wulkenhaar, Raimar. . “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. Basel: Springer International Publishing. doi: 10.1007/978-3-030-29597-4_11.
- Lionni, L, and Thürigen, J. . “Multi-critical behaviour of 4-dimensional tensor models up to order 6.” Nuclear Physics B, № 941: 600–635. doi: 10.1016/j.nuclphysb.2019.02.026.
- Grosse, Harald, and 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, and 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, and Wulkenhaar, Raimar. . “Noncommutative 3-colour scalar quantum field theory model in 2D.” The European Physical Journal C, № 78 580. doi: 10.1140/epjc/s10052-018-6042-3.
- Pérez-Sánchez, CI. . “The full Ward-Takahashi Identity for colored tensor models.” Communications in Mathematical Physics, № 358 (2): 589–632. doi: 10.1007/s00220-018-3103-2.
- Pithis, A, and Thürigen, J. . “Phase transitions in group field theory: The Landau perspective.” Physical Review D - Particles, Fields, Gravitation, and Cosmology, № 98: 126006. doi: 10.1103/PhysRevD.98.126006.
- Wulkenhaar, Raimar. . “Lambert-W solves the noncommutative \Phi^4-model.” in Vol. 15 of Oberwolfach Reports doi: 10.4171/OWR/2018/32.
- Steinhaus, S, and Thürigen, J. . “Emergence of Spacetime in a restricted Spin-foam model.” Physical Review D - Particles, Fields, Gravitation, and Cosmology, № 98: 026013. doi: 10.1103/PhysRevD.98.026013.
- Grosse, Harald, Sako, Akifumi, and 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, and 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.
- Wulkenhaar, Raimar. . “Reflection positivity in large-deformation limits of noncommutative field theories.” in Vol. 14 of Oberwolfach Reports doi: 10.4171/OWR/2017/55.
- Pérez-Sánchez, CI. . “Surgery in colored tensor models.” Journal of Geometry and Physics, № 120: 262–289. doi: 10.1016/j.geomphys.2017.06.009.
- de Jong, Jins, and Wulkenhaar, Raimar. . “The asymptotic volume of diagonal subpolytopes of symmetric stochastic matrices.” arXiv.org doi: 10.48550/arXiv.1701.07719.
- Wulkenhaar, Raimar. . “Integrability in a 4D QFT model.” in Vol. 13 of Oberwolfach Reports 13 doi: 10.4171/OWR/2016/36.
- Grosse, Harald, and Wulkenhaar, Raimar. . “Construction of a quantum field theory in four dimensions.” PoS - Proceedings of Science, № 224 151. doi: 10.22323/1.224.0151.
- Lechner, Gandalf, and Schlemmer, Jan. . “Thermal Equilibrium States for Quantum Fields on Non-commutative Spacetimes.” in Quantum Mathematical Physics , edited by Felix Finster, Johannes Kleiner, Christian Röken and Jürgen Tolksdorf. Basel: Birkhäuser Verlag. doi: 10.1007/978-3-319-26902-3.
- Grosse, Harald, and Wulkenhaar, Raimar. . “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. Basel: Springer International Publishing. doi: 10.1007/978-3-319-26902-3_8.
- Eckstein, Michał, Sitarz, Andrzej, and Wulkenhaar, Raimar. . “The Moyal sphere.” Journal of Mathematical Physics, № 2016 (57) 112301. doi: 10.1063/1.4965446.
- Thürigen, J. . “Group field theories generating polyhedral complexes.” PoS - Proceedings of Science, № FFP14: 177. doi: 10.22323/1.224.0177.
- Grosse, Harald, and Wulkenhaar, Raimar. . “On the fixed point equation of a solvable 4D QFT model.” Vietnam Journal of Mathematics, № 2016 (44): 153–180. doi: 10.1007/s10013-015-0174-7.
- Ousmane Samary, Dine, Pérez-Sánchez, Carlos Ignacio, Vignes-Tourneret, Fabien, and Wulkenhaar, Raimar. . “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.
- Thürigen, J. . “Discrete quantum geometries and their effective dimension.” Dissertation thesis, Humboldt Universität zu Berlin. doi: 10.18452/17309.
- Thürigen, J. . “Fields and Laplacians on Quantum Geometries.” in Proceedings, 13th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories (MG13): Stockholm, Sweden, July 1-7, 2012 doi: 10.1142/9789814623995_0388.
- Calcagni, G, Oriti, D, and Thürigen, J. . “Dimensional flow in discrete quantum geometries.” Physical Review D - Particles, Fields, Gravitation, and Cosmology, № 91 (8): 084047. doi: 10.1103/PhysRevD.91.084047.
- Oriti, D, Ryan, JP, and Thürigen, J. . “Group field theories for all loop quantum gravity.” New Journal of Physics, № 17: 023042. doi: 10.1088/1367-2630/17/2/023042.
- Grosse, Harald, and Wulkenhaar, Raimar. . “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. Krakau: Copernicus Center Press.
- Grosse, Harald, and Wulkenhaar, Raimar. . “Noncommutative quantum field theory.” Fortschritte der Physik, № 62 (9-10): 797–811. doi: 10.1002/prop.201400020.
- Grosse, Harald, and Wulkenhaar, Raimar. . “Solvable 4D noncommutative QFT: phase transitions and quest for reflection positivity.” arXiv doi: 10.48550/arXiv.1406.7755.
- Grosse, Harald, and Wulkenhaar, Raimar. . “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. . “Construction of the \Phi^4_4-quantum field theory on noncommutative Moyal space.” RIMS Kôkyûroku, № 2014 (1904): 67–104.
- Calcagni, G, Oriti, D, and Thürigen, J. . “Spectral dimension of quantum geometries.” Class. Quant. Grav., № 31: 135014. doi: 10.1088/0264-9381/31/13/135014.
- Gayral, Victor, and Wulkenhaar, Raimar. . “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. . “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. . “Solvable limits of a 4D noncommutative QFT.” arXiv doi: 10.48550/arXiv.1306.2816.
- Grosse, Harald, and 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, 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.
- Calcagni, G, Oriti, D, and Thurigen, J. . “Laplacians on discrete and quantum geometries.” Class. Quant. Grav., № 30: 125006. doi: 10.1088/0264-9381/30/12/125006.
- Spisso, Bernardino, and Wulkenhaar, Raimar. . “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. . “Renormalization of a noncommutative field theory.” International Journal of Modern Physics A, № 27 (12) 1250067. doi: 10.1142/S0217751X12500674.
- Grosse, Harald, and Wulkenhaar, Raimar. . “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. . “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. . “Renormalizable noncommutative quantum field theory.” Journal of Physics: Conference Series, № 343 012043. doi: 10.1088/1742-6596/343/1/012043.
- Grosse, Harald, and Wulkenhaar, Raimar. . “Renormalisation of the Grosse-Wulkenhaar model.” PoS - Proceedings of Science, № QGQGS (2011) 011.
- Grosse, Harald, and 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.” in Vol. 7 of Oberwolfach Reports doi: 10.4171/OWR/2010/09.
- Wulkenhaar, Raimar. . “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.
- Wulkenhaar, Raimar. . “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. . “Progress in solving a noncommutative quantum field theory in four dimensions.” arXiv doi: 10.48550/arXiv.0909.1389.
- Marcillaud, de Goursac A, Wallet, JC, and Wulkenhaar, R. . “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.
- Grosse, Harald, and Wulkenhaar, Raimar. . “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.
- Gayral, Victor, Jureit, Jan-Hendrik, Krajewski, Thomas, and Wulkenhaar, Raimar. . “Quantum field theory on projective modules.” Journal of Noncommutative Geometry, № 1 (4): 431–496. doi: 10.4171/JNCG/13.
- Marcillaud de Goursac, Axel, Jean-Christophe, Wallet, and Wulkenhaar, Raimar. . “Noncommutative induced gauge theory.” European Physical Journal C: Particles and Fields, № 51 (4): 977–987. doi: 10.1140/epjc/s10052-007-0335-2.
- Grosse, Harald, and Wulkenhaar, Raimar. . “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.
- Wulkenhaar, Raimar. . “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.
- Wulkenhaar, Raimar. . “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. . “Noncommutative QFT and renormalization.” Fortschritte der Physik, № 54 (2-3): 116–123. doi: 10.1002/prop.200510260.
- Grosse, Harald, and Wulkenhaar, Raimar. . “Noncommutative QFT and renormalization.” Bulgarian Journal of Physics, № 33 (s1): 215–225.
- Rivasseau, Vincent, Vignes-Tourneret, Fabien, and Wulkenhaar, Raimar. . “Renormalisation of noncommutative ϕ4-theory by multi-scale analysis.” Communications in Mathematical Physics, № 262 (3): 565–594. doi: 10.1007/s00220-005-1440-4.