157 citations · 1.5k across the 35 of their papers we have counts for
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Magic Relations and Critical Varieties of Feynman Integrals
Giulio Crisanti, Hjalte Frellesvig, Andrzej Pokraka +1
Magic relations are a class of integration-by-parts identities where all integrals in the generating sector drop out. Since their presence causes several otherwise successful metho…
The spectrum of Feynman-integral geometries at two loops
Piotr Bargiela, Hjalte Frellesvig, Robin Marzucca +4
We provide a complete classification of the Feynman-integral geometries at two-loop order in four-dimensional Quantum Field Theory with standard quadratic propagators. Concretely,…
Classification of Feynman integral geometries for black-hole scattering at 5PM order
Daniel Brammer, Hjalte Frellesvig, Roger Morales +1
We provide a complete classification of the Feynman integral geometries relevant to the scattering of two black holes at fifth order in the post-Minkowskian (PM) expansion, i.e. at…
Calabi-Yau Feynman integrals in gravity: -factorized form for apparent singularities
Hjalte Frellesvig, Roger Morales, Sebastian Pögel +2
We study a recently identified four-loop Feynman integral that contains a three-dimensional Calabi-Yau geometry and contributes to the scattering of black holes in classical gravit…
The Loop-by-Loop Baikov Representation -- Strategies and Implementation
Hjalte Frellesvig
In this paper, we discuss the Baikov representation of Feynman integrals in its standard and loop-by-loop variants. The Baikov representation is a parametric representation, which…
Classifying post-Minkowskian geometries for gravitational waves via loop-by-loop Baikov
Hjalte Frellesvig, Roger Morales, Matthias Wilhelm
We use the loop-by-loop Baikov representation to investigate the geometries in Feynman integrals contributing to the classical dynamics of a black-hole two-body system in the post-…
Intersection Numbers, Polynomial Division and Relative Cohomology
Giacomo Brunello, Vsevolod Chestnov, Giulio Crisanti +3
We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential -forms, by combining the advantages emerging from the choice o…
Calabi-Yau meets Gravity: A Calabi-Yau three-fold at fifth post-Minkowskian order
Hjalte Frellesvig, Roger Morales, Matthias Wilhelm
We study geometries occurring in Feynman integrals that contribute to the scattering of black holes in the post-Minkowskian expansion. These geometries become relevant to gravitati…
On -factorised bases and pure Feynman integrals
Hjalte Frellesvig, Stefan Weinzierl
We investigate -factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals…
Intersection Numbers from Higher-order Partial Differential Equations
Vsevolod Chestnov, Hjalte Frellesvig, Federico Gasparotto +2
We propose a new method for the evaluation of intersection numbers for twisted meromorphic -forms, through Stokes' theorem in dimensions. It is based on the solution of an $…
On Epsilon Factorized Differential Equations for Elliptic Feynman Integrals
Hjalte Frellesvig
In this paper we develop and demonstrate a method to obtain epsilon factorized differential equations for elliptic Feynman integrals. This method works by choosing an integral basi…
Cuts and Isogenies
Hjalte Frellesvig, Cristian Vergu, Matthias Volk +1
We consider the genus-one curves which arise in the cuts of the sunrise and in the elliptic double-box Feynman integrals. We compute and compare invariants of these curves in a num…
Decomposition of Feynman Integrals by Multivariate Intersection Numbers
Hjalte Frellesvig, Federico Gasparotto, Stefano Laporta +4
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation…
Vector Space of Feynman Integrals and Multivariate Intersection Numbers
Hjalte Frellesvig, Federico Gasparotto, Manoj K. Mandal +3
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multiv…
Generalized Polylogarithms in Maple
Hjalte Frellesvig
This paper describes generalized polylogarithms, multiple polylogarithms, and multiple zeta values, along with their implementation in Maple 2018. This set of related functions is…