Effective field theory for highly ionized plasmas

We examine the equilibrium properties of hot, non-relativistic plasmas. The partition function and density correlation functions of a plasma with seve ral species are expressed in terms of a functional integral over electrosta tic potential distributions. This is a convenient formulation for performin g a perturbative expansion. The theory is made well-defined at every stage by employing dimensional regularization which, among other virtues, automat ically removes the unphysical (infinite) Coulomb self-energy contributions. The leading order, held-theoretic tree approximation automatically include s the effects of Debye screening. No further partial resummations are neede d for this effect. Subleading, one-loop corrections are easily evaluated. T he two-loop corrections, however, have ultraviolet divergences. These corre spond to the short-distance, logarithmic divergence which is encountered in the spatial integral of the Boltzmann exponential when it is expanded to t hird order in the Coulomb potential. Such divergences do not appear in the underlying quantum theory - they are rendered finite by quantum fluctuation s. We show how such divergences may be removed and the correct finite theor y obtained by introducing additional local interactions in the manner of od ern effective quantum field theories. We compute the two-loop induced coupl ing by exploiting a non-compact su(1, 1) symmetry of the hydrogen atom. Thi s enables us to obtain explicit results for density-density correlation fun ctions through two-loop order and thermodynamic quantities through three-lo op order. The induced couplings are shown to obey renormalization group equ ations, and these equations are used to characterize all leading logarithmi c contributions in the theory. A linear combination of pressure plus energy and number densities is shown to be described by a field-theoretic anomaly . The effective Lagrangian method that we employ yields a simple demonstrat ion that, at long distance, correlation functions have an algebraic fall of f (because of quantum effects) rather than the exponential damping of class ical Debye screening. We use the effective theory to compute, easily and ex plicitly, this leading long-distance behavior of density correlation functi ons. The presentation is pedagogical and self-contained. The results for th ermodynamic quantities at three-loop [or O(n(5/2))] order, and for the lead ing long-distance forms of correlation functions, agree with previous resul ts in the literature, but they are obtained in a novel and simple fashion u sing the effective held theory. In addition to the new construction of the effective field theory for plasma physics, we believe that the results we r eport for the explicit form of correlation functions at two-loop order, as well as the determination of higher-order leading-logarithmic contributions , are also original. (C) 2001 Elsevier Science B.V. All rights reserved.