Perturbation theory of non-perturbative Yang-Mills theory: a massive expansion from first principles

The main objective of this thesis is to present a new analytical framework for low-energy QCD that goes under the name of massive, or "screened", perturbative expansion. The massive perturbative expansion is motivated by the phenomenon of dynamical mass generation, by which the gluons acquire a mass of the order of the QCD scale $\Lambda_{\text{QCD}}$ in the limit of vanishing momentum. It is a simple extension of ordinary perturbation theory that consists in a shift of the expansion point of the Yang-Mills perturbative series with the aim of treating the transverse gluons as massive already at tree-level, while leaving the total action of the theory unchanged. The new framework will be formulated in the context of pure Yang-Mills theory, where the lattice data is readily available for comparison and the perturbative results have been perfected by enforcing the gauge invariance of the analytical structure of the gluon propagator.