相关论文: On a class of Feynman integrals evaluating to iter…

We study the analytic continuation of Feynman integrals from the kite family, expressed in terms of elliptic generalisations of (multiple) polylogarithms. Expressed in this way, the Feynman integrals are functions of two periods of an…

We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman…

We derive gradient and second order {\em a priori} estimates for solutions of the Neumann problem for a general class of fully nonlinear elliptic equations on compact Riemannian manifolds with boundary. These estimates yield regularity and…

We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The…

We show that momentum space Feynman diagrams involving internal massless fields can be cast as conformal integrals. This leads to a classification of all Feynman diagrams into conformal families, labelled by conformal integrals. Computing…

We describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…

We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a…

We propose a construction of generalized cuts of Feynman integrals as an operation on the domain of the Feynman parametric integral. A set of on-shell conditions removes the corresponding boundary components of the integration domain, in…

We describe iterated integrals as unipotent periods on families of marked elliptic curves in terms of multiple zeta values and elliptic multiple zeta values.

A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…

This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.

These are expanded lecture notes from lectures given at the Workshop on higher structures at MATRIX Melbourne. These notes give an introduction to Feynman categories and their applications. Feynman categories give a universal categorical…

The modular spaces are a family of polarizations of the Hilbert space that are based on Aharonov's modular variables and carry a rich geometric structure. We construct here, step by step, a Feynman path integral for the quantum harmonic…

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…

A recursion formula is derived which allows to evaluate invariant integrals over the orthogonal group O(N), where the integrand is an arbitrary finite monomial in the matrix elements of the group. The value of such an integral is…

In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…

We derive residue formulas for the regularized integrals (introduced by Li-Zhou) on configuration spaces of elliptic curves. Based on these formulas, we prove that the regularized integrals satisfy holomorphic anomaly equations, providing a…