A Gauge-Invariant Reorganization of Thermal Gauge Theory
This dissertation is devoted to the study of thermodynamics for quantum gaugetheories. The poor convergence of quantum field theory at finite temperaturehas been the main obstacle in the practical applications of thermal QCD fordecades. In this dissertation I apply hard-thermal-loop perturbation theory,which is a gauge-invariant reorganization of the conventional perturbativeexpansion for quantum gauge theories to the thermodynamics of QED andYang-Mills theory to three-loop order. For the Abelian case, I present acalculation of the free energy of a hot gas of electrons and photons byexpanding 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 thecoupling constant. I demonstrate that the hard-thermal-loop perturbationreorganization improves the convergence of the successive approximations to theQED free energy at large coupling, $e \sim 2$. For the non-Abelian case, Ipresent a calculation of the free energy of a hot gas of gluons by expanding ina 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-loopperturbation theory is compatible with lattice results for the pressure, energydensity, and entropy down to temperatures $T \sim 2-3\;T_c$. The resultssuggest that HTLpt provides a systematic framework that can be used tocalculate static and dynamic quantities for temperatures relevant at LHC.