Related papers: Tropical Feynman integration in the physical regio…
We apply tropical geometry to study the image of a map defined by Laurent polynomials with generic coefficients. If this image is a hypersurface then our approach gives a construction of its Newton polytope.
We describe an additional module for the Mathematica package FeynRules that allows for an easy building of any N=1 supersymmetric quantum field theory, directly in superspace. After the superfield content of a specific model has been…
A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different…
We present a detailed study of the combinatorial interpretation of matrix integrals, including the examples of tessellations of arbitrary genera, and loop models on random surfaces. After reviewing their methods of solution, we apply these…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
Describing the combinatorial structure of the tropical complex $C$ of a tropical matroid polytope, we obtain a formula for the coarse types of the maximal cells of $C$. Due to the connection between tropical complexes and resolutions of…
We recall the question of geometric integrators in the context of Poisson geometry, and explain their construction. These Poisson integrators are tested in some mechanical examples. Their properties are illustrated numerically and they are…
Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of the classical Onishchik's lists \cite{onish1} and we…
High precision calculations in perturbative QFT often require evaluation of big collection of Feynman integrals. Complexity of this task can be greatly reduced via the usage of linear identities among Feynman integrals. Based on…
The worldline formalism allows one to obtain compact integral representations combining the information of large numbers of Feynman diagrams. However, their analytic calculation leads to a non-standard integration problem for which existing…
FeynRules is a Mathematica-based package which addresses the implementation of particle physics models, which are given in the form of a list of fields, parameters and a Lagrangian, into high-energy physics tools. It calculates the…
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)…
We elaborate on the method of differential equations for evaluating Feynman integrals. We focus on systems of equations for master integrals having a linear dependence on the dimensional parameter. For these systems we identify the criteria…
We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
We review a method for the algebraic treatment of a family of functions which contains the multiple polylogarithms, with applications to the symbolic calculation of Feynman integrals.
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…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
FeynMaster is a multi-tasking software for particle physics studies. By making use of already existing programs (FeynRules, QGRAF, FeynCalc), FeynMaster automatically generates Feynman rules, generates and draws Feynman diagrams, generates…