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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 $m_D/T$, $m_f/T$ and $e^2$, where $m_D$ and $m_f$ 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, $e \sim 2$. 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 $m_D/T$ and $g^2$, where $m_D$ 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 $T \sim 2-3\;T_c$. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC.