Interacting Elementary Excitations in Ultrarelativistic Plasmas: Damping Mechanisms and Plasma Thermodynamics
This dissertation examines the properties of the elementary excitations in quark-gluon and electromagnetic plasmas. Due to Debye screening and Landau damping mechanisms, the interaction fields fall off at large distances, except for static magnetic and color-magnetic fields. The lack of screening of the magnetic interaction leads to a singularity at small momentum transfer in the matrix element for fermion-fermion scattering via the exchange of a single gluon, or a single photon. We analyze the effects of this singularity on the quasiparticle lifetimes in plasmas at zero and at finite temperature T. First, at T = 0, we find that the fermion excitations above the ground state are long-lived, as the Pauli exclusion principle limits the collision phase space. Because the magnetic interaction is long-ranged, the damping rates of the excitations near the edge of the Fermi sea vary linearly with the excitation energy. The quasiparticles are therefore not as well- defined as those encountered in non-relativistic plasmas, with short-ranged interactions, where the variation of the damping rates away from the Fermi surface is quadratic, thus slower. Second, we find that in plasmas at finite temperatures, the magnetic interaction introduces correlations between the successive scatterings of the fermion quasiparticles on the charges in the system. This effect leads to a decay law that decreases in time more rapidly than an exponential; however the quasiparticles are long-lived. We also derive a framework for ascertaining the effects of the long-ranged magnetic interaction on the thermodynamic properties of relativistic plasmas. Our method generalizes the concept of conserving, phi-derivable, approximations to relativistic field theories. By treating the interaction field as a dynamical degree of freedom, we are able to derive the thermodynamical potential in terms of full propagators. This approach allows us to resolve the entropy into contributions from its interacting elementary excitations.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign