Effective Field Theory for Highly Ionized Plasmas

Abstract

We examine the equilibrium properties of hot, dilute, non-relativistic plasmas. The partition function and density correlation functions of a classical plasma with several species are expressed in terms of a functional integral over electrostatic potential distributions. The leading order, field-theoretic tree approximation automatically includes the effects of Debye screening. Subleading, one-loop corrections are easily evaluated. The two-loop corrections, however, have ultraviolet divergences. These correspond to the short-distance, logarithmic divergence which is encountered in the spatial integral of the Boltzmann exponential when it is expanded to third order in the Coulomb potential. Such divergences do not appear in the underlying quantum theory --- they are rendered finite by quantum fluctuations. We show how such divergences may be removed and the correct finite theory obtained by introducing additional local interactions in the manner of modern effective quantum field theories. We obtain explicit results for density-density correlation functions through two-loop order and thermodynamic quantities through three-loop order. The induced couplings are shown to obey renormalization group equations, and these equations are used to characterize all leading logarithmic contributions in the theory. A linear combination of pressure and energy and number densities is shown to be described by a field-theoretic anomaly. The effective theory allows us to evaluate very easily the algebraic long-distance decay of density correlation functions.