Kubo formulas for relativistic fluids in strong magnetic fields

TL;DR

This paper derives the transport coefficients for relativistic magnetized fluids, accounting for symmetry breaking by magnetic fields, and relates them to equilibrium correlation functions using non-equilibrium statistical methods.

Contribution

It provides a comprehensive set of transport coefficients for magnetized relativistic fluids, including shear, bulk viscosities, and thermal conductivities, derived consistently with fundamental principles.

Findings

Derived complete transport coefficient set for magnetized fluids.

Expressed coefficients in terms of equilibrium Green's functions.

Identified five shear and two bulk viscosities in the dissipative function.

Abstract

Magnetohydrodynamics of strongly magnetized relativistic fluids is derived in the ideal and dissipative cases, taking into account the breaking of spatial symmetries by a quantizing magnetic field. A complete set of transport coefficients, consistent with the Curie and Onsager principles, is derived for thermal conduction, as well as shear and bulk viscosities. It is shown that in the most general case the dissipative function contains five shear viscosities, two bulk viscosities, and three thermal conductivity coefficients. We use Zubarev's non-equilibrium statistical operator method to relate these transport coefficients to correlation functions of equilibrium theory. The desired relations emerge at linear order in the expansion of the non-equilibrium statistical operator with respect to the gradients of relevant statistical parameters (temperature, chemical potential, and velocity.) The transport coefficients are cast in a form that can be conveniently computed using equilibrium (imaginary-time) infrared Green's functions defined with respect to the equilibrium statistical operator.