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In recent years enormous progress has been made in perturbative quantum field theory by applying methods of algebraic geometry to parametric Feynman integrals for scalar theories. The transition to gauge theories is complicated not only by…

Mathematical Physics · Physics 2017-09-14 Marcel Golz

The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the method of differential equations has proven…

High Energy Physics - Phenomenology · Physics 2018-02-08 Christoph Meyer

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…

High Energy Physics - Phenomenology · Physics 2020-03-18 Costas G. Papadopoulos , Christopher Wever

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 program FeynRules is a Mathematica package developed to facilitate the implementation of new physics theories into high-energy physics tools. Starting from a minimal set of information such as the model gauge symmetries, its particle…

High Energy Physics - Phenomenology · Physics 2014-06-13 Adam Alloul , Neil D. Christensen , Celine Degrande , Claude Duhr , Benjamin Fuks

We define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand, which we…

High Energy Physics - Phenomenology · Physics 2019-01-17 Martijn Hidding , Francesco Moriello

It was observed that hyperlogarithms provide a tool to carry out Feynman integrals. So far, this method has been applied successfully to finite single-scale processes. However, it can be employed in more general situations. We give examples…

High Energy Physics - Theory · Physics 2014-04-01 Erik Panzer

Inspired by the work of Feynman, Deutsch, We formally propose the theory of physical computability and accordingly, the physical complexity theory. To achieve this, a framework that can evaluate almost all forms of computation using various…

Computational Physics · Physics 2011-12-06 Huimin Zheng , HaiXing Hu , Nan Wu , Fangmin Song

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…

High Energy Physics - Phenomenology · Physics 2015-06-03 Alexey Pak

The volume and the number of lattice points of the permutohedron P_n are given by certain multivariate polynomials that have remarkable combinatorial properties. We give several different formulas for these polynomials. We also study a more…

Combinatorics · Mathematics 2007-05-23 Alexander Postnikov

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…

High Energy Physics - Theory · Physics 2016-07-08 Kasper J. Larsen , Yang Zhang

We uncover a combinatorial structure governing the differential equations satisfied by wavefunction coefficients of scalar fields with generic masses in de Sitter space. Using an integral representation of the massive mode functions, we…

High Energy Physics - Theory · Physics 2026-04-13 Daniel Baumann , Austin Joyce , Hayden Lee , Kamran Salehi Vaziri

We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface in the Macaulay2 package NumericalNP.m2. We propose a tropical membership test, relying on this algorithm, for…

Algebraic Geometry · Mathematics 2018-11-30 Taylor Brysiewicz

In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an…

High Energy Physics - Theory · Physics 2023-03-22 B. Ananthanarayan , Sumit Banik , Souvik Bera , Sudeepan Datta

We investigate the behaviour of elliptic Feynman integrals under modular transformations. This has a practical motivation: Through a suitable modular transformation we can achieve that the nome squared is a small quantity, leading to fast…

High Energy Physics - Theory · Physics 2021-02-24 Stefan Weinzierl

Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and especially the definition and study of an…

High Energy Physics - Theory · Physics 2015-07-07 Barak Kol

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…

High Energy Physics - Phenomenology · Physics 2007-05-23 A. V. Kotikov

A generalized-ensemble technique, multicanonical sampling, is used to study the folding of a 34-residue human parathyroid hormone fragment. An all-atom model of the peptide is employed and the protein-solvent interactions are approximated…

Statistical Mechanics · Physics 2009-11-10 Ulrich H. E. Hansmann

This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled by the Feynman-Vernon model. The user gives the program a vector describing the coordinate of an open quantum system, a hamiltonian…

Quantum Physics · Physics 2015-06-05 Nikesh S. Dattani

We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The…

High Energy Physics - Phenomenology · Physics 2021-06-02 Moritz Walden , Stefan Weinzierl