A gauge-invariant reorganization of thermal gauge theory

This dissertation is devoted to the study of thermodynamics for quantum gauge theories.The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in mD/T, mf /T and e2, where mD and mf are the photon and electron thermal masses, respectively, and e is the coupling constant.I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e ~ 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in mD/T and g2, where mD is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T ~ 2 - 3 Tc. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC.Die Dissertation ist aufgebaut auf den folgenden Veröffentlichungen: • J. O. Andersen, M. Strickland and N. Su Three-loop HTL free energy for QED Physical Review D 80, 085015 (2009) • J. O. Andersen, M. Strickland and N. Su Gluon Thermodynamics at Intermediate Coupling Physical Review Letters 104, 122003 (2010) • J. O. Andersen, M. Strickland and N. Su Three-loop HTL gluon thermodynamics at intermediate coupling arXiv:1005.1603 [hep-ph] (Eingereicht zu Händen des Journal of High Energy Physics