nLab
transseries

Contents

Idea

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

In application to perturbative quantum field theory one is interested in functions of the coupling constant gg and the relevant expansions are in terms of x=gx=g or x=g 2x=g^2 and z 1=xz_1=x for the contributions of the Feynman perturbation series and z 2=e c/xz_2=e^{-c/x} for capturing non-perturbative effects. Also z 3=logx/x 0z_3=\log x/x_0.

Reference

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

Last revised on February 10, 2018 at 14:11:17. See the history of this page for a list of all contributions to it.