Statistics and Sampling of Feynman periods

This is a large numerics and statistics project where we computed millions of Feynman integrals and developed a new efficient sampling algorithm to compute their average at large loop order.

Tubing solutions to Dyson-Schwinger equations

The renormalization structure of Feynman graphs implies that the perturbative Green functions of a theory can be organized in terms of power series of rooted trees. So far, it had been tedious to recover the actual (numerical or symbolic) coefficients of an analytic Green function from those trees. We show that this can be done with a nice combinatorial operation, namely by enumerating all the tubings of the tree in question.

Renormalization conditions and Resurgence

Many renormalization schemes, including minimal subtraction, can be expressed as variants of kinematic renormalization. This opens a whole new approach to analytic treatment of their Green functions. For a certain class of model Dyson-Schwinger equations, we determined the asymptotic growth of their series solutions and compared it for different renormalization schemes.

Diffeomorphisms of quantum field variables

A non-linear redefinition of the field variable in a qft gives rise to complicated new interaction terms, which eventually do not contribute to the onshell S-matrix. Moreover, diffeomorphisms have the same power-counting as quantum gravity and serve as a toy model for Ward identities under such conditions.