Dr. Benjamin Knorr

Postdoctoral Researcher
Radboud University, Nijmegen

I am a postdoctoral researcher at the Institute for Mathematics, Astrophysics, and Particle Physics of the Radboud University in Nijmegen. My main research focus is on theoretical high energy physics (THEF), in particular Quantum Gravity, but also on phase transitions in condensed matter systems and numerical methods.

The goal of my research is to formulate a consistent theory of quantum gravity with modern renormalisation group methods, but without introducing new degrees of freedom. This naturally links different approaches to quantum gravity, in particular Asymptotic Safety and Causal Dynamical Triangulations. Surprisingly, the same methods are applicable to practically any quantum theory or statistical system. One application is to predict universal critical exponents in second order phase transitions.

Currently I'm a member of the quantum gravity group headed by Prof. Renate Loll, and work closely with Prof. Frank Saueressig. I've received my doctorate at the Friedrich-Schiller University Jena under the supervision of Prof. Andreas Wipf.

I'm organising the Quantum Gravity Lunch Seminar - if you want to speak there, send me an e-mail.


Research Interests

For a long time, only quantum field theories which are perturbatively renormalisable were considered "good" theories. More recently, this attitude changed - more and more well-behaving, predictive theories were found which are not asymptotically free, but controlled by an ultraviolet fixed point of its renormalisation group flow. Such theories are called asymptotically safe. An open question, and central point of my research is whether quantum gravity is asymptotically safe.
With modern functional renormalisation group techniques, I'm investigating several topics in this approach to quantum gravity, including

  • the role of diffeomorphism invariance and bimetric calculations,
  • backgrounds suitable for the calculation of renormalisation group equations,
  • form factors governing the scale dependence of interactions,
  • its connection to other approaches of quantum gravity, in particular causal dynamical triangulations.

To do so, I employ state-of-the-art analytical and numerical tools: the Mathematica package xAct and pseudo-spectral methods. Not only can one study quantum field theories with these tools, but also condensed matter systems. A side interest of mine is the study of theories which are relevant in these systems, for example in the description of phase diagrams in Dirac materials.

Explanations for some of my work aimed at the general public can be found here.


All my publications can be found on inspire. As part of my open science policy, my papers are freely available on the arXiv. Both are linked in the navigation on the right, as is my ORCID identifier. Some key articles:

Towards reconstructing the quantum effective action of gravity

B. Knorr and F. Saueressig

This work provides a new systematic approach connecting the fundamental formulation of the theory of quantum gravity to its effective dynamics. First-hand evidence for the appearance of non-local interactions in quantum gravity relevant for cosmological model-building is presented.

Gravitational Two-Loop Counterterm Is Asymptotically Safe

H. Gies, B. Knorr, S. Lippoldt and F. Saueressig

The renormalisation group flow of the Einstein-Hilbert action supplemented by the two-loop counterterm found by Goroff and Sagnotti exhibits the non-Gaussian fixed point crucial for Asymptotic Safety. The new operator corresponds to an irrelevant direction and does not introduce a undetermined coupling constant.

Global solutions of functional fixed point equations via pseudospectral methods

J. Borchardt and B. Knorr

Pseudospectral methods are systematically introduced in the context of the functional renormalisation group. They are shown to be suitable to resolve fixed point functions globally, to high accuracy and efficiently.

Ising and Gross-Neveu model in next-to-leading order

B. Knorr

The 3d Gross-Neveu model is reconsidered in a significantly improved approximation. Critical quantities are calculated, and change mildly compared to earlier works. This indicates an extraordinary convergence of the derivative expansion in this model.

Selected Talks

Here is a selection of talks I gave.

Is Lorentz symmetry relevant?

Veldhoven '19

Physics@Veldhoven '19

Towards reconstructing the quantum effective action of gravity

Paris '18

International Conference on the Exact Renormalization Group (ERG 2018)

Diffeomorphism invariance in Asymptotic Safety

Nijmegen '17

Quantum Gravity lunch seminar

Gross-Neveu-Yukawa models at criticality

Bremen '17

DPG Spring Meeting

The problem of quantising gravity, and how to possibly overcome it

Freiburg '16

Seminar on Fundamental Interactions



Click on the envelope on the bottom of the right panel.

Visiting address

Huygens Building
Room HG02.068
Heyendaalseweg 135
6525 AJ Nijmegen
The Netherlands

Postal address

IMAPP - Faculty of Science
P.O. Box 9010
6500 GL Nijmegen
The Netherlands
Radboud Universiteit