%0 Generic
%A Haas, Michael
%D 2014
%F heidok:17875
%R 10.11588/heidok.00017875
%T Spectral functions in finite temperature SU(3) gauge theory and applications to transport phenomena
%U https://archiv.ub.uni-heidelberg.de/volltextserver/17875/
%X In this thesis, gluon spectral functions in SU(3) gauge theory are calculated  at finite temperature. The temperature range covers the confining regime below Tc to  the high temperature regime, where perturbation theory is applicable. The numerical  tool is the Maximum Entropy Method (MEM) employing euclidean, non-perturbative,  Landau gauge gluon propagators, obtained with the Functional Renormalisation Group  and Lattice QCD, as input. The spectral function is related to the propagators by an  integral equation. MEM is a complex multidimensional optimisation algorithm to invert  such integral equations, corresponding to an analytic continuation of the numerical  data. A continuation of a discreet set of data cannot be unambiguous. The occuring  ambiguities are resolved by introducing a priori knowledge of the asymptotic shape of  the spectral function, in the form of a model function. Thereby, MEM simultaneously  optimizes the spectral function to the input propagators and the model, leading to a  unique model-dependent solution. Standard-MEM assumes positive definite spectral  functions, whereas gluons show a violation of positivity in the spectral function, due  to confinement. Therefore, an extended-MEM algorithm is proposed. The main application  of this thesis is the calculation of the shear viscosity in units of the entropy  density. A Kubo relation connects shear viscosity to the low frequency limit of a certain  energy-momentum tensor correlation function. For this correlation function a loop representation  of finite order in terms of gluon spectral functions is derived. That allows to  calculate eta/s from first principles in SU(3) for the first time for arbitrary temperatures.  Further, a mapping of the SU(3) results for eta/s to QCD is proposed.