Explicit analytical expressions are derived for the gluon propagator in a generic linear covariant R ξ gauge, by a screened massive expansion for the exact Faddeev-Popov Lagrangian of pure Yang-Mills theory. At one-loop, if the gauge invariance of the pole structure is enforced, the gluon dressing function is entirely and uniquely determined, without any free parameter or external input. The gluon propagator is found finite in the IR for any ξ, with a slight decrease of its limit value when going from the Landau gauge (ξ ¼ 0) toward the Feynman gauge (ξ ¼ 1). An excellent agreement is found with the lattice in the range 0 < ξ < 0.5 where the data are available.

A very simple variational approach to pure SUðNÞ Yang-Mills theory is proposed, based on the Gaussian effective potential in a linear covariant gauge. The method provides an analytical variational argument for mass generation. The method can be improved order by order by a perturbative massive expansion around the optimal trial vacuum. At finite temperature, a weak first-order transition is found (at T c ≈ 250 MeV for N ¼ 3) where the mass scale drops discontinuously. Above the transition the optimal mass increases linearly as expected for deconfined bosons. The equation of state is found in good agreement with the lattice data.

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The objective of this thesis is to present two new perturbative frameworks for the study of low-energy Quantum Chromodynamics (QCD), termed the Screened Massive Expansion and the Dynamical Model. Both the frameworks paint a picture of the infrared regime of QCD which is consistent with the current knowledge provided by the lattice calculations and by other non-perturbative methods, displaying dynamical mass generation in the gluon sector and a massless ghost propagator. The Screened Massive Expansion achieves this by operating a shift of the QCD perturbative series, performed by adding a mass term for the transverse gluons in the kinetic part of the Faddeev-Popov Lagrangian and subtracting it back from its interaction part so that the total action remains unchanged. The Dynamical Model, on the other hand, interprets the generation of a dynamical mass for the gluons as being triggered by a non-vanishing condensate of the form ⟨(A h ) 2 ⟩, where A h is a gaugeand BRST-invariant non-local version of the gluon field, and explores the consequences of the inclusion of the former in the partition function of the theory. Since the main focus of this thesis is on the gauge sector of QCD, most of our calculations will be carried out in the context of pure Yang-Mills theory. There we will show that the gluon and the ghost propagator derived by making use of the two frameworks are in good agreement with the Euclidean Landau-gauge lattice data, within the limits of a one-loop approximation. During the course of the thesis we will address topics such as the first-principles status of the two methods, the absence of Landau poles from the strong running coupling constant and the extension of the Screened Massive Expansion to finite temperatures and to full QCD. Future research prospects are discussed in the Conclusions.