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A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly)…

High Energy Physics - Phenomenology · Physics 2011-05-05 A. Ferroglia , G. Passarino , M. Passera , S. Uccirati

We review the method of uniqueness which is a powerful technique for multi-loop calculations in higher dimensional theories with conformal symmetry. We use the method in momentum space and show that it allows a very transparent evaluation…

High Energy Physics - Theory · Physics 2017-04-06 S. Teber , A. V. Kotikov

We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…

High Energy Physics - Theory · Physics 2019-03-06 Pierpaolo Mastrolia , Sebastian Mizera

Using functional derivatives with respect to free propagators and interactions we derive a closed set of Schwinger-Dyson equations in quantum electrodynamics. Its conversion to graphical recursion relations allows us to systematically…

High Energy Physics - Theory · Physics 2015-06-26 Axel Pelster , Hagen Kleinert , Michael Bachmann

In this paper, we study the singularities of Feynman integrals using homological techniques. We analyse the Feynman integrals by compactifying the integration domain as well as the ambient space by embedding them in higher-dimensional…

High Energy Physics - Theory · Physics 2024-02-06 Tanay Pathak , Ramesh Sreekantan

We present a simple trick that allows to consider the sum of all connected Feynman diagrams at fixed position of interaction vertices for general fermionic models. With our approach one achieves superior performance compared to Diagrammatic…

Strongly Correlated Electrons · Physics 2017-08-02 Riccardo Rossi

The operator approach to analytical evaluation of multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of massless Feynman integrals, such as the integration by parts method and the method of…

High Energy Physics - Theory · Physics 2008-11-26 A. P. Isaev

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…

High Energy Physics - Phenomenology · Physics 2022-10-12 Bo Feng , Jianyu Gong , Tingfei Li

When calculating higher terms of the epsilon-expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with…

High Energy Physics - Theory · Physics 2008-11-26 A. I. Davydychev , M. Yu. Kalmykov

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…

Machine Learning · Computer Science 2020-12-17 Silviu-Marian Udrescu , Andrew Tan , Jiahai Feng , Orisvaldo Neto , Tailin Wu , Max Tegmark

We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…

High Energy Physics - Phenomenology · Physics 2021-04-21 Guy R. Jehu

Unveiling hidden symmetries within Feynman diagrams is crucial for achieving more efficient computations in high-energy physics. In this paper, we study the symmetries underlying the causal Loop-Tree Duality (LTD) representations through a…

High Energy Physics - Theory · Physics 2025-05-12 Irene Lopez Imaz , German Sborlini

The purpose of this paper is to show that, under certain combinatorial conditions on the graph, parametric Feynman integrals can be realized as periods on the complement of the determinant hypersurface in an affine space depending on the…

Algebraic Geometry · Mathematics 2012-04-11 Paolo Aluffi , Matilde Marcolli

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…

High Energy Physics - Phenomenology · Physics 2024-09-02 Vladyslav Shtabovenko , Rolf Mertig , Frederik Orellana

The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…

High Energy Physics - Phenomenology · Physics 2007-05-23 E. Mendels

This paper continues our previous study of Feynman integrals in configuration spaces and their algebro-geometric and motivic aspects. We consider here both massless and massive Feynman amplitudes, from the point of view of potential theory.…

Mathematical Physics · Physics 2013-08-28 Ozgur Ceyhan , Matilde Marcolli

Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…

Using dispersive techniques, it is possible to avoid ultraviolet divergences in the calculation of Feynman diagrams, making subsequent regularization of divergent diagrams unnecessary. We give a simple introduction to the most important…

High Energy Physics - Theory · Physics 2009-11-10 Andreas Aste , Dirk Trautmann

A T-dualized selfdual inspired formulation of massive vector fields coupled to arbitrary matter is generated; subsequently its perturbative series modeling a spontaneously broken gauge theory is analyzed. The new Feynman rules and external…

High Energy Physics - Theory · Physics 2009-11-07 Gordon Chalmers , Warren Siegel

By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore…

High Energy Physics - Phenomenology · Physics 2019-04-17 Xiao Liu , Yan-Qing Ma