Related papers: Non-planar Feynman integrals, Mellin-Barnes repres…
Integrative modeling of macromolecular assemblies allows for structural characterization of large assemblies that are recalcitrant to direct experimental observation. A Bayesian inference approach facilitates combining data from…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
The method of Mellin-Barnes representation is used to calculate dimensionally regularized massive on-shell double box Feynman diagrams contributing to Bhabha scattering at two loops.
Work is reported on finite integral representations for 2-loop massive 2-, 3- and 4-point functions, using orthogonal and parallel space variables. It is shown that this can be utilized to cover particles with arbitrary spin (tensor…
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…
By merging algorithmic Matsubara integration with discrete pole representations we present a procedure to generate fully analytic closed form results for impurity problems at fixed perturbation order. To demonstrate the utility of this…
Kernel Bayesian inference is a principled approach to nonparametric inference in probabilistic graphical models, where probabilistic relationships between variables are learned from data in a nonparametric manner. Various algorithms of…
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do {\it not} request special choices of bases.…
In this survey, we review some of the recent connections between the representation theory of (untwisted) quantum affine algebras and the representation theory of current algebras. We mainly focus on the finite-dimensional representations…
Multimodal summarization integrating information from diverse data modalities presents a promising solution to aid the understanding of information within various processes. However, the application and advantages of multimodal…
In theories like SM or MSSM with a complex gauge group structure the complete set of Feynman diagrams contributed to a particular physics process can be splited to exact gauge invariant subsets. Arguments and examples given in the review…
Tree-level Feynman diagrams in a cubic scalar theory can be given a metric such that each edge has a length. The space of metric trees is made out of orthants joined where a tree degenerates. Here we restrict to planar trees since each…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…
In these lectures we introduce the Feynman-Schwinger representation method for solving nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving…
In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth…
In previous two papers, we defined fractional Brauer configuration algebras and developed their covering theory. In this paper, we study the representation theory of fractional Brauer graph algebras of type MS, a special class of fractional…
Using a Mellin-Barnes representation, we compute the on-shell massless planar double box Feynman diagram with an irreducible scalar product of loop momenta in the numerator. This diagram is needed in calculations of two loop corrections to…
We discuss the possibility to solve Modern Numerical Relativity problems using finite element methods (FEM). Adopting a "user friendly" software for handling totally general systems of nonlinear partial differential equations, FEMLAB, we…
We consider methods for constructing explicit solutions of the non-stationary Lam\'e equation, which is a generalization of the classical Lam\'e equation, that has appeared in works on integrable models, conformal field theory, high energy…