The lattice quark propagator at finite temperature - Leal Júnior, Jesuel Marques (2024)
Quantum Chromodynamics (QCD) is the theory currently used to describe the strong interaction between quarks and gluons. One of the characteristic features of the theory is its behavior at high energies, where the small coupling between the particles allows for the safe application of traditional quantum field theory techniques, such as perturbative expansions. Conversely, at low energies, the coupling grows and perturbative methods break down. The defining features in the low-energy regime are confinement and spontaneous chiral symmetry breaking. A satisfactory theoretical explanation of these infrared phenomena is still lacking, although a consensus has formed that the use of non-perturbative tools is imperative in their study. An interesting laboratory to explore confinement and chiral symmetry breaking is the environment described by QCD at high temperatures, as the theory is found to undergo chiral symmetry restoration and also a transition to a quark-gluon plasma. In this plasma the fundamental particles are found to be deconfined but strongly interacting. The Greens functions (also called N-point functions or correlators) of the theory encapsulate information relevant to the description of the aforementioned non-perturbative low-energy phenomena. The primary objective of this thesis was the calculation of a particular correlator, the quark propagator, in the vacuum and at finite temperatures. To this end, we have performed numerical simulations using the non-perturbative framework of Lattice Quantum Chromodynamics, which presents a discretized and Euclidean version of QCD, preserving the internal SU(3) gauge symmetry of the theory exactly. We have used the quenched approximation and produced ensembles of gauge configurations for several lattice volumes and temperatures. The quark propagator was computed in the vacuum and at temperatures above the deconfinement transition. A necessary step in the study of correlators in general, and propagators in particular, is setting up a gauge fixing scheme. As a valuable by-product of this project, we have refined and optimized algorithms for SU(3) gauge fixing to Landau gauge on the lattice. In this thesis, we present the approach of Lattice Quantum Chromodynamics, including the introduction of fermions on the lattice and the algorithms employed in the simulations. Our findings encompass the thermal effects on the quark propagator, as well as the results of the Landau gauge fixing optimizations.