Dynamics of Gauge Fields at High Temperature

An effective description of dynamical Bose fields is provided by the classical (high-temperature) limit of thermal field theory. The main subject of this thesis is to improve the ensuing classical field theory, that is, to include the dominant quantum corrections and to add counter terms for the Rayleigh-Jeans divergences. The dominant quantum corrections are the well-known hard thermal loops. After a diagrammatic calculation of the HTL photon self-energy in QED, a kinetic formulation of HTL's is given, following the work of Blaizot and Iancu. It is shown that the classical HTL equation of motion is consistent with the classical statistical theory, provided a random noise term is added.
For both SU(N) gauge theory and scalar field theory with a lambda^4 interaction term, it is demonstrated that the the Rayleigh-Jeans divergences are restricted to one- and two-loop (sub)diagrams. This implies that the proof of Aarts and Smit that local mass counter terms render classical \lambda^4-theory finite up to two loops, may be extended to any number of loops. It will be shown that classical one-loop diagrams that correspond to HTL's in the quantum theory lead to linear divergences; all other one-loop diagrams are finite in the classical theory. A general argument is presented that two-loop diagrams can at most give logarithmic divergences. This is explicitly verified for two-loop self-energy corrections in SU(N) and scalar theories. We also use the Ward identities to show that the logarithmic divergence in the SU(N) self-energy is transverse. It has been surmised that subtraction in the plasmon frequency is sufficient to render the theory free of linear divergences at one loop. This is confirmed and also that beyond one-loop linear divergences are absent. Furthermore the introduction of counter terms for classical lattice theories is investigated. It is found that to match a classical to a quantum theory is less complicated then to match a lattice theory to a continuum one. Nevertheless, in the latter case approximate counter terms can be given. In the final chapter, a different topic is approached, namely the problem of explaining the baryon asymmetry in the early universe. Usually the required CP-violation is induced in a model by an effective dimension-six operator. In the thesis the effect of dimension-eight CP-violating operators on sphaleron transitions is studied. It is argued that in a pure gauge theory in equilibrium the distribution function of the Chern-Simons number (that is related to the baryon number) will develop an asymmetry. Also a scenario for baryogenesis is presented where this effect is utilized.