Related papers: Feynman integrals and multiple polylogarithms
There are three kinds of multiple polylogarithms; complex, finite and symmetric. The dualities for the complex and finite cases are known. In this paper, we present proofs of them via iterated integrals and its symmetric counterpart by a…
We initiate a systematic framework for the analysis of analytic properties of finite Feynman integrals that are multiple polylogarithms. Based on the Feynman parameter representation in complex projective space, we make a complete…
We present a new method for the decomposition of multi-loop Euclidean Feynman integrals into quasi-finite Feynman integrals. These are defined in shifted dimensions with higher powers of the propagators, make explicit both infrared and…
The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…
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…
Operads and PROPs are presented, together with examples and applications to quantum physics suggesting the structure of Feynman categories/PROPs and the corresponding algebras.
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…
Starting with univariate polynomial interpolation we arrive to a natural generalization of fundamental theorem of algebra for certain systems of multivariate algebraic equations.
In this talk I discuss properties of the two Symanzik polynomials which characterise the integrand of an arbitrary multi-loop integral in its Feynman parametric form. Based on the construction from spanning forests and Laplacian matrices,…
An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this…
This study is targeted to the NLO corrections of multileg processes, very important for the LHC. Starting from the construction of Feynman diagrams, the analytical reduction of general one-loop integrals to scalar master ones, the…
We discuss some of the problems that may occur in the calculation of complicated Feynman diagrams. These include the group independent evaluation of color factors, and the summation techniques that are needed for the expansion of diagrams…
Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path…
A Feymnan integral is computed exactly using LLL
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…
In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.
We initiate a systematic study of one-loop integrals by investigating the connection between their singularity structures and geometric configurations in the projective space associated to their Feynman parametrization. We analyze these…
A transformation on homogeneous polynomials is proposed, which is further applied to parametric Feynman integrals. The two representations related through this transformation are dual to each other. It naturally leads to dualities of Landau…
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…
We present a loop-by-loop method for computing the differential equations of Feynman integrals using the recently developed dual form formalism. We give explicit prescriptions for the loop-by-loop fibration of multi-loop dual forms. Then,…