Static and dynamic properties of QCD at finite temperature
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Abstract
In this work we study strongly interacting matter at finite temperature. We consider Quantum Chromodynamics (QCD) mainly with two degenerate flavors of quarks below the phase transition. We rely on the Lattice approach to treat QCD in the non-perturbative regime. In this framework, the inclusion of finite temperature is fairly straightforward but extracting real-time properties from the Monte Carlo data is a non-trivial problem. The focus of the work is put on the pion quasiparticle. In particular we investigate the change in its dispersion relation due to thermal effects and compare it to the vacuum situation. At low momenta, the dispersion relation depends on a Renormalization Group Invariant (RGI) parameter u(T) called the pion velocity' that can be calculated in terms of screening (or static) quantities. Those can be calculated with standard numerical techniques. We calculate the pion velocity for several values of the temperature at different quark masses and find strong evidence that boost invariance is violated due to thermal effects. Our findings are in qualitative agreement with analytic calculations in Chiral Perturbation Theory (ChPT). In addition, we explore a method to access information in spectral functions: the Backus-Gilbert method which has never been applied to QCD before and has the advantage over more traditional methods that a model-independent estimator for the spectral function can be defined. As a complementary project, we investigate SU(3) pure Yang-Mills theory with shifted boundary conditions. We use the latter to determine the renormalization constant of the off-diagonal elements of the energy-momentum-tensor at various values of the bare coupling. This constant is crucial for taking the continuum limit of energy-momentum-tensor-correlators from which transport properties of the system can be derived.