相关论文: On factorization hierarchy of equations for banana…
We continue the development of a position space approach to equations for Feynman multi-loop integrals. The key idea of the approach is that unintegrated products of Greens functions in position space are still loop integral in momentum…
We propose the extension of the position space approach to Feynman integrals from the banana family to generic Feynman diagrams. Our approach is based on getting rid of integration in position space and then writing differential equations…
In this talk we discuss the construction of a basis of master integrals for the family of the $l$-loop equal-mass banana integrals, such that the differential equation is in an $\varepsilon$-factorised form. As the $l$-loop banana integral…
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the…
The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties.…
This expository text is an invitation to the relation between quantum field theory Feynman integrals and periods. We first describe the relation between the Feynman parametrization of loop amplitudes and world-line methods, by explaining…
We provide a comprehensive summary of concepts from Calabi-Yau motives relevant to the computation of multi-loop Feynman integrals. From this we derive several consequences for multi-loop integrals in general, and we illustrate them on the…
We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can…
We report on three improvements in the context of Feynman integral reduction and $\varepsilon$-factorised differential equations: Firstly, we show that with a specific choice of prefactors, we trivialise the $\varepsilon$-dependence of the…
Dimensionally or analytically regulated Feynman integrals lead to relative twisted period integrals. We present a recent extension of the Griffiths-Dwork pole reduction algorithm for deriving the D-module of differential operators acting on…
We extend the study of banana diagrams in coordinate representation to the case of curved space-times. If the space is harmonic, the Green functions continue to depend on a single variable -- the geodesic distance. But now this dependence…
Starting from the Mellin-Barnes integral representation of a Feynman integral depending on set of kinematic variables $z_i$, we derive a system of partial differential equations w.r.t.\ new variables $x_j$, which parameterize the…
In this paper, we give a detailed account of the algorithm outlined in [1] for Feynman integral reduction and $\varepsilon$-factorised differential equations. The algorithm consists of two steps. In the first step, we use a new geometric…
We compute the three-loop banana integral with four unequal masses in dimensional regularisation. This integral is associated to a family of K3 surfaces, thus representing an example for Feynman integrals with geometries beyond elliptic…
We outline ideas to connect the analytic structure of Feynman amplitudes to the structure of Karen Vogtmann's {\em Outer Space}. We focus on the role of cubical chain complexes in this context, and also investigate the bordification problem…
In this talk, we use several examples to elaborate on how a recently proposed algorithm can turn non-trivial Feynman integrals into an $\varepsilon $-factorised manner, regardless of their hidden geometric essence. In particular, some extra…
We generalise a method recently introduced in the literature, that derives canonical differential equations, to multi-scale Feynman integrals with an underlying Calabi-Yau geometry. We start by recomputing a canonical form for the sunrise…
This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory.…
We consider the calculation of the master integrals of the three-loop massive banana graph. In the case of equal internal masses, the graph is reduced to three master integrals which satisfy an irreducible system of three coupled linear…
I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…