transseries

**analysis** (differential/integral calculus, functional analysis, topology)

metric space, normed vector space

open ball, open subset, neighbourhood

convergence, limit of a sequence

compactness, sequential compactness

continuous metric space valued function on compact metric space is uniformly continuous

…

…

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 $z_3=\log x/x_0$.

- 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.