Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations

18Citations
Citations of this article
10Readers
Mendeley users who have this article in their library.

Abstract

Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that the MIs fulfil linear systems of coupled differential equations in the external invariants. With the increase in number of loops and external legs, one is left in general with an increasing number of MIs and consequently also with an increasing number of coupled differential equations, which can turn out to be very difficult to solve. In this paper we show how studying the IBPs in fixed integer numbers of dimension d = n with n∈N one can extract the information useful to determine a new basis of MIs, whose differential equations decouple as d→n and can therefore be more easily solved as Laurent expansion in (d-n).

Cite

CITATION STYLE

APA

Tancredi, L. (2015). Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations. Nuclear Physics B, 901, 282–317. https://doi.org/10.1016/j.nuclphysb.2015.10.015

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free