Anmerkungen:
Tag der Verteidigung: 09.10.2023
Zusammenfassungen in deutscher und englischer Sprache
Beschreibung:
In this thesis, we concentrate on the sector of QCD that does not include quarks, i.e. pure Yang-Mills, for which we investigate different BRST-invariant realizations in perturbative and non-perturbative settings. Such an analysis yields information regarding long-range physics and the effect of BRST symmetry. For the perturbative treatment, following the off-shell prescription of the Faddeev-Popov quantization, we set up a gauge-fixing action that is linear in the gauge-fixing condition by choosing instead of the conventional Gaussian, a Fourier weight. Then, by employing the background field method we construct an IR regulated background and BRST-invariant action. This is achieved by an appropriate choice of a non-linear gauge-fixing condition that includes regulator-mass parameters. A one-loop perturbative analysis of the effective action leads to the universal one-loop beta function. The effects of the mass parameters are explored with a phenomenological study of the action density. Hence, assuming covariantly constant and self-dual backgrounds, we observe the presence of a non-trivial minimum which is justified as a manifestation of dynamical breaking of scale symmetry and an indication of a gluon condensate. Furthermore, an explicit investigation of the one-loop Schwinger functional is carried. For the non-perturbative treatment, we concern ourselves with the extension of the model to mass-dependent renormalization schemes and more precisely within the functional Renormalization Group. In the absence of a background field, we derive a beta function that can be aligned with the universal one-loop beta function. In the presence of a background field, we find, without additional restrictions, a truncated flow equation which is similar to the one found in the literature that reproduces proper universal results up to two-loop order.