Perturbations vs deformations
Published: Apr 16, 2025
Last Updated: Apr 16, 2025
Authors:Maksim Gritskov, Andrey Losev
Abstract
In the first part of the paper we define a perturbative (pre-formal) geometry and formulate a theorem on the relation between the construction of a perturbative neighborhood of affine varieties and the higher tangent bundles. In the second part of the paper, we discuss perturbative vector fields and related structures, which are finite-dimensional analogs of perturbation theory characteristics arising in quantum field theory.