Related papers: Partial fractioning reduction of perturbative ampl…
We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these…
We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…
The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in $d = 4 - 2\epsilon$ dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces,…
The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…
A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
We present an algorithm of the reduction of the differential equations for master integrals the Fuchsian form with the right-hand side matrix linearly depending on dimensional regularization parameter $\epsilon$. We consider linear…
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
While traditional implementations of variable-length digital delay lines are based on a circular buffer accessed by two pointers, we propose an implementation where a single fractional pointer is used both for read and write operations. On…
An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example.
Exactly computing the full output distribution of linear optical circuits remains a challenge, as existing methods are either time-efficient but memory-intensive or memory-efficient but slow. Moreover, any realistic simulation must account…