Thermal Gauge Theory for a Rotating Plasma

TL;DR

The paper develops a complete, gauge-invariant thermal field theory for generic equilibrium density matrices that include average angular momentum, extending to all gauge theories. Using a path-integral formalism with both real- and imaginary-time contours, it derives generalized KMS conditions for arbitrary representations and computes all thermal propagators for scalars, gauge fields, and Faddeev-Popov ghosts in the presence of rotation and chemical potentials. A key result is that, in perturbation theory, only propagators are modified by the rotation and chemical potentials; the interaction vertices remain the same as in the non-rotating, zero-chemical-potential case, simplifying practical calculations via established perturbative tools. The framework is model-independent and readily applicable to a wide range of gauge theories, including those relevant to rotating astrophysical plasmas and color-superconducting phases in QCD, thus offering a versatile toolkit for finite-temperature, rotating systems.

Abstract

This paper provides a systematic and complete study of thermal gauge theory for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also of average angular momentum. This work extends previous studies, which focused on pure scalar-fermion theories, to all gauge theories coupled to an arbitrary matter sector. Path-integral methods are developed to study ensemble averages and thermal Green's functions of general operators, with an arbitrary number of points, in all interacting gauge theories. These methods cover both the real-time and imaginary-time formalisms. Generalized Kubo-Martin-Schwinger (KMS) conditions are obtained both in coordinate and in momentum space for operators in general representations of the Lorentz and internal symmetry group. This allows us to obtain all thermal propagators including those of gauge fields and Faddeev-Popov ghosts. By analyzing all interactions in detail, it is shown that, in perturbation theory, only the propagators are affected by the average angular momentum and the chemical potentials, the vertices remain unmodified. The paper presents fully model-independent results and can, therefore, be applied to any specific thermal field theory.