相关论文: Feynman integrals and iterated integrals of modula…

It is shown that every Feynman integral can be interpreted as Green function of some linear differential operator with constant coefficients. This definition is equivalent to usual one but needs no regularization and application of…

We study the algebra $\mathcal{I}^{QM}$ of iterated integrals of quasimodular forms for $\operatorname{SL}_2(\mathbb{Z})$, which is the smallest extension of the algebra $QM_{\ast}$ of quasimodular forms, which is closed under integration.…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the…

In this talk I review the connections between Feynman integrals and multiple polylogarithms. After an introductory section on loop integrals I discuss the Mellin-Barnes transformation and shuffle algebras. In a subsequent section multiple…

We present generic expressions for the integrands of canonical bases under maximal cut in elliptic Feynman integral families with multiple kinematic scales. Such integrals frequently arise in phenomenologically relevant scattering…

We identify two families of ten-point Feynman diagrams that generalize the elliptic double box, and show that they can be expressed in terms of the same class of elliptic multiple polylogarithms to all loop orders. Interestingly, one of…

We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…

Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each…

We show that some Lorentz components of the Feynman integrals calculated in terms of the light-cone variables may contain end-point singularities which originate from the contribution of the big-circle integral in the complex k_ plane.…

It is known that multiple zeta values can be written in terms of certain iterated log-sine integrals. Conversely, we evaluate iterated log-sine integrals in terms of multiple polylogarithms and multiple zeta values in this paper. We also…

In this talk we discuss how ideas from the theory of mixed Hodge structures can be used to find differential equations for Feynman integrals. In particular we discuss the two-loop sunrise graph in two dimensions and show that these methods…

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

We show how to construct a complete set of lowering operators, whose successive application reduces an arbitrary Fenyman integral to a combination of master integrals. The construction builds systems of equations for generic integral…

In this paper, we explore the recursive structure of Baikov representations for Feynman integrals. We demonstrate that the various Baikov representations for all sectors of an integral family can be organized in a tree-like structure. Using…

This work deals with two types of Feynman integrals in perturbative quantum field theory: the 2-loop 2-point kite, with 5 arbitrary internal masses, and its completion by a sixth propagator, to give a 3-loop tetrahedral tadpole, with 6…

We consider the most general two-loop massless correlator $I(n_1,n_2,n_3,n_4,n_5; x,y;D)$ of two composite vertices with the Bjorken fractions $x$ and $y$ for arbitrary indices $\{n_i\}$ and space-time dimension $D$; this correlator is…

A Feymnan integral is computed exactly using LLL

The Compositional Integral is defined, formally constructed, and discussed. A direct generalization of Riemann's construction of the integral; it is intended as an alternative way of looking at First Order Differential Equations. This brief…