One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized Bosonic and Fermionic systems

TL;DR

This paper derives new quantum field theoretical expressions for shear and bulk viscosities of hot charged bosonic and fermionic systems in magnetic fields using the one-loop Kubo formalism, highlighting differences from kinetic theory results.

Contribution

It introduces a novel quantum field theoretical approach to calculate viscosities in magnetic fields, connecting relaxation time and Landau level transitions with spectral function widths.

Findings

Derived explicit thermo-magnetic spectral functions for viscosities.

Found differences between Kubo and kinetic theory expressions in magnetic fields.

Connected kinetic theory parameters with spectral function features.

Abstract

The expressions of the shear viscosity and the bulk viscosity components in the presence of an arbitrary external magnetic field for a system of hot charged scalar Bosons (spin-0) as well as for a system of hot charged Dirac Fermions (spin-$\frac{1}{2}$) have been derived by employing the one-loop Kubo Formalism. This is done by explicitly evaluating the thermo-magnetic spectral functions of the energy momentum tensors using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In the present work, a rich quantum field theoretical structure in the expressions of the viscous coefficients in non-zero magnetic field are found, which are different from their respective expressions obtained earlier via kinetic theory based calculations; though, in absence of magnetic field, the one-loop Kubo and the kinetic theory based expressions for the viscosities are known to be identical. We have identified that Kubo and kinetic theory based results of viscosity components follow similar kind of temperature and magnetic field dependency. The relaxation time and the synchrotron frequency in the kinetic theory formalism are realized to be connected respectively with the thermal width of propagator and the transitions among the Landau levels of the charged particles in the Kubo formalism. We believe that, the connection of latter quantities are quite new and probably the present work is the first time addressing this interpretation along with the new expressions of viscosity components, not seen in existing works.