Prof. Dirk Kreimer

Prof. Kreimer erforscht grundlegende mathematische Strukturen der Quantenfeldtheorie, insbesondere die Eichabhängigkeit von Green-Funktionen und deren Beschreibung durch Dyson-Schwinger-Gleichungen. Sein aktueller Fokus liegt auf modernen algebraischen Methoden — speziell der Hopf-Algebra-Theorie und Hochschild-Kohomologie — um zu verstehen, wie physikalische Größen in der Quantenfeldtheorie von der Wahl der Eichung abhängen oder unabhängig sind. Diese Grundlagenforschung trägt zur mathematischen Fundierung von Quantenfeldtheorien bei, die in der Teilchenphysik und theoretischen Physik zentral sind.

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• Kolleg Mathematik Physik Berlin

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  The Kolleg Mathematik Physik Berlin is an interdisciplinary center at Humboldt-Universität zu Berlin. Its community of research groups shares a mutual interest in Mathematics and Physics. Quantum field theory is their unifying theme, which connects to algebraic geometry, number theory and differential geometry in mathematics, as well as to research in particle physics, gravitation and string theory in physics.Since the advent of the SFB 647 Space-Time-Matter, founded through enormous efforts by Jochen Bruening, there has been common scientific interest in the Berlin area in interdisciplinary research between mathematics and physics.This was recognised in the creation of a bridge professorship between the two disciplines for Matthias Staudacher, and boosted by the arrival of Alexander von Humboldt Professor Dirk Kreimer in the area. Together, the groups of Johannes Bluemlein, Francis Brown (a regular guest professor here), Hélène Esnault, Gavril Farkas, Dirk Kreimer, Klaus Mohnke, Hermann Nicolai, Jan Plefka, Matthias Staudacher and Peter Uwer now form a union of scientists with a common interest in the mathematical structures and foundations of quantum field theory and quantum gravity and its relations in particular to arithmetic and algebraic geometry, under the roof of the KMPB (Kolleg Mathematik Physik in the Berlin area).

• DAAD PRIME Fellowship: Johannes Thürigen (2016–2018)

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• International Max Planck Research School for Mathematical and Physical Aspects of Gravitation, Cosmology and Quantum Field Theory (IMPRS)

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• Angles, Scales and Parametric Renormalization

  2013

  Letters in Mathematical Physics · DOI

• Hopf algebras in renormalization theory: locality and Dyson–Schwinger equations from Hochschild cohomology

  2006

  IRMA lectures in mathematics and theoretical physics · DOI

• Resummation of infrared logarithms in de Sitter space via Dyson-Schwinger equations: The ladder-rainbow approximation

  2014

  Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology · DOI

  We study the infrared (large separation) behavior of a massless minimally coupled scalar quantum field theory with a quartic self interaction in de Sitter spacetime. We show that the perturbation series in the interaction strength is singular and secular, i.e. it does not lead to a uniform approximation of the solution in the infrared region. Only a nonperturbative resummation can capture the correct infrared behavior. We seek to justify this picture using the Dyson-Schwinger equations in the ladder-rainbow approximation. We are able to write down an ordinary differential equation obeyed by the two-point function and perform its asymptotic analysis. Indeed, while the perturbative series---truncated at any finite order---is growing in the infrared, the full nonperturbative sum can be decaying.