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Feynman integral reduction by means of integration-by-parts identities is a major power gadget in a theorist toolbox indispensable for calculation of multiloop quantum effects relevant for particle phenomenology and formal theory alike. An…
We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a…
In this talk, we discuss how ideas from geometry help to improve Feynman integral reduction and the construction of $\varepsilon$-factorised differential equations. In particular, we outline a systematic procedure to obtain an…
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…
In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
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…
Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to…
Triangle Feynman diagrams can be considered as describing form factors of states bound by a zero-range interaction. These form factors are calculated for scalar particles and compared to point-form and non-relativistic results. By examining…
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum space. Tensor integrals can directly be…
Integration by parts is used to reduce scalar Feynman integrals to master integrals.
In this manuscript, which is to appear in the proceedings of the conference "MathemAmplitude 2019" in Padova, Italy, we provide an overview of the module intersection method for the the integration-by-parts (IBP) reduction of multi-loop…
Feynman integrals are easily solved if their system of differential equations is in $\varepsilon$-form. In this letter we show by the explicit example of the kite integral family that an $\varepsilon$-form can even be achieved, if the…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop…
We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm starts with…
We present a new interface called FeynHelpers that connects FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and calculations in quantum field theory (QFT) to Package-X and FIRE. The former provides…