FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS

By M. Argeri, Pierpaolo Mastrolia. 2007

205 citations recorded by the source corpus.

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D = 4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a9c3a034cd6fe1bc1bf39156f223ee6a1aeab7c2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Nuclear and High Energy Physics

Citations in the corpus

The two-loop sunrise graph with arbitrary masses (2013, background): “We expect that a solution can be obtained along the lines of [9, 26].”
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2014, methodology): “Also within the method of differential equations [21], boundary conditions occur that must be obtained separately, e.”
Four Loop Massless Propagators: an Algebraic Evaluation of All Master Integrals (2010, background): “For its modern status and further references, see the review [97].”
The full four-loop cusp anomalous dimension in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{N} $$\end{do (2019, unknown): “We find that the differential equations (for reviews, see [63, 64]) for this basis takes the form”
Lectures on differential equations for Feynman integrals (2014, unknown): “Earlier reviews include [8].”
Magnus and Dyson series for Master Integrals (2014, methodology): “[4, 5], is one of the most effective techniques for computing dimensionally regulated multi-loop integrals and has led to significant achievements in the context of multi-loop corrections.”
Feynman integrals and hyperlogarithms (2015, methodology): “The method of differential equations [10, 98] generates a system of linear, first-order partial differential equations in terms of Feynman integrals in the family of the initial graph.”