Related papers: Why and how to use a differential equation method …
We give a pedagogical review of the application of field theoretic and path integral methods to calculate moments of the probability density function of stochastic differential equations perturbatively.
A simple systematic method for calculating derivative expansions of the one-loop effective action is presented. This method is based on using symbols of operators and well known deformation quantization theory. To demonstrate its advantages…
The unitarity method for calculating one-loop amplitudes provides algorithms of polynomial complexity. This is primarily beneficial for the computation of multi-leg one loop amplitudes and it is therefore of great interest to develop a…
The aim of this paper is a quantitative analysis of the solution set of a system of polynomial nonlinear differential equations, both in the ordinary and partial case. Therefore, we introduce the differential counting polynomial, a common…
We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package…
As the new-generation precision experiments such as MOLLER and P2 look for physics beyond Standard Model, it is becoming increasingly important to evaluate the higher-order electroweak radiative corrections to a sub-percent level of…
We derive exact, convergent representations of multiloop sunset Feynman integrals in two dimensions for arbitrary mass configurations and all loop orders valid for large Euclidean momentum. The integrals are expressed as sums of symmetric…
An overview of the solution methods for ordinary differential equations in the Mathematica function DSolve is presented.
We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…
The large moment method can be used to compute a large number of moments of physical quantities that are described by coupled systems of linear differential equations. Besides these systems the algorithm requires a certain number of initial…
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector spaces, such as functions that take as input a matrix and…
We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
In this paper we develop a new method to determine the essential spectrum of coupled systems of singular differential equations. Applications to problems from magnetohydrodynamics and astrophysics are given.
The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…
In this paper we consider multi-loop integrals appearing in MHV scattering amplitudes of planar N=4 SYM. Through particular differential operators which reduce the loop order by one, we present explicit equations for the two-loop…
We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop…
In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear…
We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…
We describe in some detail the present features of an automatic loop calculation program as well as the integration techniques that go into it. The program, called XLOOPS 1.0, allows one to calculate massive one- and two-loop Feynman…