10 papers
HyperFORM -- a FORM package for parametric integration with hyperlogarithms
Adam Kardos, Sven-Olaf Moch, Oliver Schnetz
HyperFORM brings the parametric integration of hyperlogarithms, weighted by rational prefactors, into the symbolic-manipulation system FORM. It ports the capabilities of Erik Panze…
Graphical Functions by Examples
Mrigankamauli Chakraborty, Marco Klann, Sven-Olaf Moch +4
Graphical functions have emerged as a powerful framework for evaluating multi-loop Feynman integrals in perturbative quantum field theory. Defined as massless three-point position-…
Self-duality of massless scalar three-point amplitudes
Oliver Schnetz
We prove that off-shell massless scalar three-point Feynman integrals are self-dual under Fourier transformation. This implies that a momentum space integral can be expressed as th…
LinApart2: efficient parallel partial fraction decomposition algorithm for denominators with polynomials of general degree
Levente Fekésházy, Oliver Schnetz
We present LinApart2, a major update to the LinApart algorithm for univariate partial fraction decomposition. Unlike its predecessor, LinApart2 can handle denominators of arbitrary…
HyperFORM -- a FORM package for parametric integration with hyperlogarithms
Adam Kardos, Sven-Olaf Moch, Oliver Schnetz
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation…
theory at six loops
Oliver Schnetz
We present the renormalization functions of dimensionally regularized theory in six dimensions up to loop order six in the minimal subtraction scheme.
Graphical functions with spin
Oliver Schnetz
The theory of graphical functions is generalized from scalar theories to theories with spin, leading to a numerator structure in Feynman integrals. The main part of this article tr…
The five-twist identity for Feynman periods
Oliver Schnetz
We prove a new identity for Feynman periods that acts on five-vertex cuts of completed primitive Feynman graphs. It is shown that in theory this identity is independent from…
Notes on color reductions and traces
Oliver Schnetz
We present efficient algorithms to calculate the color factors for the gauge group and to evaluate traces. The aim of these notes is to give a self-contained, proved ac…
Notes on graphical functions with numerator structure
Oliver Schnetz, Simon Theil
In these notes we generalize the theory of graphical functions from scalar theories to theories with spin.