157 citations · 494 across the 18 of their papers we have counts for
14 papers · 1 filter
Intersection matrices associated to geometric-ordered bases of Feynman integrals
Iris Bree, Federico Gasparotto, Sebastian Pögel +3
In integration-by-parts reduction of Feynman integrals, the order relation in the Laporta algorithm determines a set of master integrals. In this paper we investigate the intersect…
An algorithm towards -factorising Feynman Integrals
epsilon-collaboration, :, Iris Bree +10
In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an -factorised manner, regardless…
Improving integration-by-parts and differential equations
Iris Bree, Federico Gasparotto, Antonela Matijašić +8
In this talk, we discuss how ideas from geometry help to improve Feynman integral reduction and the construction of -factorised differential equations. In particular,…
New algorithms for Feynman integral reduction and -factorised differential equations
Iris Bree, Federico Gasparotto, Antonela Matijašić +8
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and -factorised differential equations. The algorithm consist…
The geometric bookkeeping guide to Feynman integral reduction and -factorised differential equations
Iris Bree, Federico Gasparotto, Antonela Matijašić +8
We report on three improvements in the context of Feynman integral reduction and -factorised differential equations: Firstly, we show that with a specific choice of pr…
Differential equations for tree--level cosmological correlators with massive states
Federico Gasparotto, Pouria Mazloumi, Xiaofeng Xu
We study mathematical aspects concerning two site tree-level cosmological correlators with massive internal and external states in a de Sitter universe. We employ integration by pa…
On the electron self-energy to three loops in QED
Claude Duhr, Federico Gasparotto, Christoph Nega +2
We compute the electron self-energy in Quantum Electrodynamics to three loops in terms of iterated integrals over kernels of elliptic type. We make use of the differential equation…
Lattice Correlation Functions from Differential Equations
Federico Gasparotto, Andreas Rapakoulias, Stefan Weinzierl +1
We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative reg…
Real time lattice correlation functions from differential equations
Federico Gasparotto, Stefan Weinzierl, Xiaofeng Xu
We report on an exact calculation of lattice correlation functions on a finite four-dimensional lattice with either Euclidean or Minkowskian signature. The lattice correlation func…
Non-perturbative computation of lattice correlation functions by differential equations
Federico Gasparotto, Andreas Rapakoulias, Stefan Weinzierl
We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lat…
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 $…
Macaulay Matrix for Feynman Integrals: Linear Relations and Intersection Numbers
Vsevolod Chestnov, Federico Gasparotto, Manoj K. Mandal +4
We elaborate on the connection between Gel'fand-Kapranov-Zelevinsky systems, de Rham theory for twisted cohomology groups, and Pfaffian equations for Feynman integrals. We propose…
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…