Kubo formulas for relativistic fluids in strong magnetic fields

TL;DR

This work develops covariant magnetohydrodynamics for relativistic fluids in strong magnetic fields and establishes Kubo formulas that relate dissipative transport coefficients to equilibrium correlation functions via the Zubarev non-equilibrium statistical operator. By linearizing around local equilibrium, it expresses the viscosities and thermal conductivities in terms of retarded Green's functions, with explicit decompositions in terms of $u^$, $b^$, and $b^{}$, revealing seven independent viscosities (five shear, two bulk) and three thermal conductivities under a quantizing field. The isotropic $B\to0$ limit recovers standard results, while the framework provides a principled route to compute anisotropic transport in magnetized dense matter (e.g., neutron stars) once a microscopic theory is specified. The results lay the groundwork for concrete, first-principles calculations using appropriate resummation schemes to capture infrared behavior in strongly interacting systems.

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.