Padé approximants and the prediction of non-perturbative parameters in particle physics

Abstract

Commonly used techniques to study non-perturbative aspects of the strong interactions have a deep connection with rational approximants, and in particular with Padé approximants to meromorphic functions. However, only recently this connection has been acknowledged and efforts at fully exploiting it are only starting. In this article I will briefly review the most prominent techniques used in non-perturbative strong interactions with special emphasis on its relation with Padé approximants. I will then concentrate on a set of open problems outside the scope of these conventional techniques where Padé approximants might be extremely useful.

Comments: Based on talk given at the conference "Approximation and extrapolation of convergent and divergent sequences and series", Luminy, September-October 2009. To be published in Applied Numerical Mathematics