nLab transseries

Idea

A transseries is an expansion of a function $f(x)$ as a power series in a vector $z$ whose components are fixed functions of $x$.

In application to perturbative quantum field theory one is interested in functions of the coupling constant $g$ and the relevant expansions are in terms of $x=g$ or $x=g^2$ and $z_1=x$ for the contributions of the Feynman perturbation series and $z_2=e^{-c/x}$ for capturing non-perturbative effects. Also $z_3=\log x/x_0$.

Related concepts

• asymptotic series

• resurgence theory

Reference

• Daniele Dorigoni, An Introduction to Resurgence, Trans-Series and Alien Calculus (arXiv:1411.3585)