Feynman integrals and their mathematical structure

Name of applicant

Hjalte Axel Frellesvig


University of Copenhagen


DKK 1,197,809



Type of grant

Reintegration Fellowships


The behaviour of elementary particles - the smallest constituents of matter - is described by the Standard Model of particle physics. The goal of my research, and of the current project, is to use the Standard Model to make high precision physical predictions for the outcome of elementary particle collisions, as they take place for instance at CERN's LHC collider. In particular the focus will be on a certain mathematical object - the Feynman integral - in terms of which such predictions are naturally formulated, and the project is focused on the computation of these objects along with an investigation of their mathematical structure. Another underlying objective is to make the computations of high precision physical predictions as automatic and streamlined as possible.


With the ongoing experiments at CERN's LHC collider, the standard model of particle physics is experimentally verified better than ever before. As potential new physics may appear as subtle discrepancies between theory and experiment, the theoretical uncertainties have to be kept below the ever decreasing experimental ones, and to ensure this, high precision calculations of the sort this project is concerned with have to be made. In addition to the impact on the search for new physics, a better understanding of Feynman integrals and scattering amplitudes will help shed light on structures and simplifications in the results of the predictions, of a kind that are not evident or even expected based on the traditional formulations of the theory.


My work is purely theoretical, and relies on physical theory and mathematics to make predictions for particle physics experiments. Specifically the theory of elementary particles is formulated in an abstract mathematical language (that of perturbative quantum field theory), and to make predictions based on the theory, it has to be applied in a form that is sufficiently concrete to be implemented on a computer, something that demands the use of both advanced mathematical and computational techniques. One prominent approach to be used for this project, is based on the mathematical field of "intersection theory", which can help with the deduction of relations between Feynman integrals, something that has been bottleneck in many current state-of-the-art calculations.

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