Hard thermal loops in the real-time formalism

TL;DR

This paper systematically extends the hard thermal loop effective theory to the real-time formalism, revealing additional fluctuation amplitudes and providing graphical rules, thus connecting quantum field theory with classical plasma physics.

Contribution

It introduces a comprehensive real-time HTL framework, including a second set of amplitudes for charge fluctuations, and offers graphical rules for their calculation.

Findings

Real-time HTL includes a second set of amplitudes for charge fluctuations.

Graphical rules are provided for generating HTL functions.

The theory relates quantum gauge theory to classical plasma physics.

Abstract

We present a systematic discussion of Braaten and Pisarski's hard thermal loop (HTL) effective theory within the framework of the real-time (Schwinger-Keldysh) formalism. As is well known, the standard imaginary-time HTL amplitudes for hot gauge theory express the polarization of a medium made out of nonabelian charged point-particles; we show that the complete real-time HTL theory includes, in addition, a second set of amplitudes which account for Gaussian fluctuations in the charge distributions, but nothing else. We give a concise set of graphical rules which generate both set of functions, and discuss its relation to classical plasma physics.