Dr. Johannes Thürigen, Mathematisches Institut

Member of Mathematics Münster

I am a DFG funded researcher in the Mathematical Physics group interested in renormalization and its algebraic structure in quantum field theory, in particular combinatorially non-local theories with applications to random geometry and quantum gravity. You can find more information here .

Research InterestsTensor/Group field theory
Renormalization and Hopf algebras
Renormalization group
Quantum gravity
Current Talks Wave Function Renormalizations in Non-Local Field Theories. DPG-Frühjahrstagung 2024, Berlin Slides Link to event
The Phase Space of Field Theories with Tensorial Interactions. Lorentzian Quantum Gravity: Renormalization Group and Phase Structure, Center for Advanced Studies, LMU München
4D Geometry Generated by Combinatorially Non-local Field Theory. Quantum Gravity 2023, Nijmegen Slides Link to event
Quantum Geometry & the Functional Renormalization Group in Tensorial Field Theory. QFT Seminar, Institute for Theoretical Physics, FSU Jena Link to event
What numbers in combinatorially non-local field theory?. Period Seminar, Mathematical Institute, University of Oxford
Flowing from Tensor Field Theory to Tensor Models. Quantum Gravity and Random Geometry, Paris Slides Link to event
Three Ways to Mean-Field Group Field Theory. Quantum gravity, hydrodynamics and emergent cosmology, München Link to event
Dimensional reduction along the RG flow in combinatorially non-local field theories. 11th International Conference on the Exact Renormalization Group 2022, Berlin Slides Link to event
Local-Potential Approximation in Tensor-Invariant Theories. Tensor Journal Club, Paris (virtual) Slides Link to event
Current PublicationsBen Geloun, J; Pithis, A; Thürigen, J QFT with Tensorial and Local Degrees of Freedom: Phase Structure from Functional Renormalization. Journal of Mathematical Physics Vol. 65, 2024 online
Marchetti, L; Oriti, D; Pithis, A; Thürigen, J Phase transitions in TGFT: a Landau-Ginzburg analysis of Lorentzian quantum geometric models. Journal of High Energy Physics (JHEP) Vol. 02, 2023 online
Marchetti, L; Oriti, D; Pithis, A; Thürigen, J Mean-Field Phase Transitions in TGFT Quantum Gravity. Physical Review Letters Vol. 130, 2023 online
Jercher, A; Steinhaus, S; Thürigen, J Curvature effects in the spectral dimension of spin foams. Physical Review D (PRD) Vol. 108, 2023 online
Brunekreef, J; Lionni, L; Thürigen, J One-matrix differential reformulation of two-matrix models. Reviews in Mathematical Physics Vol. 34 (08), 2022 online
Pithis AG, Thürigen J (No) phase transition in tensorial group field theory. Physics Letters B Vol. 816, 2021, pp 136215 online
Thürigen, J Renormalization in Combinatorially Non-Local Field Theories: the BPHZ Momentum Scheme. Symmetry, Integrability and Geometry: Methods and Applications Vol. 17, 2021 online
Thürigen J Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs. Math. Phys. Anal. Geom. Vol. 24 (2), 2021 online
Marchetti L, Oriti D, Pithis A, Thürigen J Phase transitions in tensorial group field theories: Landau-Ginzburg analysis of models with both local and non-local degrees of freedom. JHEP Vol. 12 (2021), 2021, pp 201 online
Current ProjectsNon-perturbative Group field theory from combinatorial Dyson-Schwinger equations and their algebraic structure II

One of the greatest theoretical challenges in fundamental physics is to combine general relativity and quantum field theory to a quantum theory of gravity. Quantum field theories on non-commutative geometry have recently been found to be solvable non-perturbatively in a matrix-theory representation. Group field theory is a generalization of such matrix field theory to higher rank and is a candidate for a quantum theory of gravity. It is therefore an important question to what extent non-perturbative solutions can be obtained in group field theory as well. In this research project we address this challenge making use of the algebraic structure of renormalization on the level of Dyson-Schwinger equations. Quantum symmetries related both to the tensorial structure as well as the gauge invariance of the theory allow to simplify these equations. In this way we will find under which conditions group field theory can be solved non-perturbatively and derive solutions. Control over the non-perturbative regime is an open issue of huge physical interest since the limit to continuum space-time coincides with the limit to critical loci in such a theory of quantum gravity.

online
E-Mailjohannes dot thuerigen at uni-muenster dot de
Phone+49 251 83-33905
Room306, OR 12
Secretary   Sekretariat Dierkes
Frau Gabi Dierkes
Telefon +49 251 83-33730
Zimmer 414
AddressDr. Johannes Thürigen
Mathematisches Institut
Fachbereich Mathematik und Informatik der Universität Münster
Einsteinstrasse 62
48149 Münster
Deutschland
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