Related papers: Differential Reduction Algorithms for Hypergeometr…
In this paper we consider systems of partial (multidimensional) linear difference equations. Specifically, such systems arise in scientific computing under discretization of linear partial differential equations and in computational high…
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 $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions.…
A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop…
We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find…
We present a novel benchmark application of a quantum algorithm to Feynman loop integrals. The two on-shell states of a Feynman propagator are identified with the two states of a qubit and a quantum algorithm is used to unfold the causal…
An algorithm for obtaining the Taylor coefficients of an expansion of Feynman diagrams is proposed. It is based on recurrence relations which can be applied to the propagator as well as to the vertex diagrams. As an application, several…
We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…
The flexible method of reduction to finite integrals, briefly described in earlier publications of the author, is described in detail. The method is suitable for the calculation of all quantum electrodynamical contributions to the magnetic…
We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
A new approach is introduced to study QCD amplitudes at high energy and comparatively small momentum transfer. Novel cut diagrams, representing resummation of Feynman diagrams, are used to simplify calculation and to avoid delicate…
We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…
Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…
A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V.…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
A new method is developed to calculate multiloop Feynman diagrams in non-relativistic field theories. A consistent scheme for regularizing and renormalizing loop integrals is established and shown to reproduce the results of dimensional…
For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle…
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at…