A real-time thermal field theoretical analysis of Kubo-type shear viscosity : Numerical understanding with simple examples

Abstract

A real-time thermal field theoretical calculation of shear viscosity has been described in the Kubo formalism for bosonic and fermionic medium. The two point function of viscous stress tensor in the lowest order provides one-loop skeleton diagram of boson or fermion field for bosonic or fermionic matter. According to the traditional diagrammatic technique of transport coefficients, the finite thermal width of boson or fermion is introduced in their internal lines during the evaluation of boson-boson or fermion-fermion loop diagram. These thermal widths of $\varphi$ boson and $\psi$ fermion are respectively obtained from the imaginary part of self-energy for $\varphi \Phi$ and $\psi \Phi$ loops, where interactions of higher mass $\Phi$ boson with $\varphi$ and $\psi$ are governed by the simple $\varphi \varphi \Phi$ and ${\ovψ}ψΦ$ interaction Lagrangian densities. A two-loop diagram, having same power of coupling constant as in the one-loop diagram, is deduced and its contribution appears much lower than the one-loop values of shear viscosity. Therefore the one-loop results of Kubo-type shear viscosity may be considered as leading order results for this simple $\varphi \varphi \Phi$ and ${\ovψ}ψΦ$ interactions. This approximation is valid for any values of coupling constant and at the temperatures greater than the mass of constituent particles of the medium.

References in corpus (5)

• Shear Viscosity of a Hot Pion Gas
• Effect of spectral modification of $\rho$ on shear viscosity of a pion gas
• Real-time propagators at finite temperature and chemical potential
• Transport coefficients in Chiral Perturbation Theory
• Transport properties of a meson gas

Cited by in corpus (16)

• Electrical conductivity and Hall conductivity of hot and dense hadron gas in a magnetic field: a relaxation time approach
• The nucleon thermal width due to pion-baryon loops and its contribution in Shear viscosity
• Electrical conductivity of hadronic matter from different possible mesonic and baryonic thermal fluctuations
• Magneto-Seebeck coefficient and Nernst coefficient of hot and dense hadron gas
• One-loop Kubo estimations of the shear and bulk viscous coefficients for hot and magnetized Bosonic and Fermionic systems
• Chiral phase structure and sixteen meson states in SU(3) Polyakov linear-sigma model at finite temperature and chemical potential in strong magnetic field
• Effect of time-varying electromagnetic field on Wiedemann-Franz law in a hot hadronic matter
• Quantum version of transport coefficients in Nambu--Jona-Lasinio model at finite temperature and strong magnetic field
• Diffusion matrix associated with the diffusion processes of multiple conserved charges in a hot and dense hadronic matter
• Chirality dependence in charge and heat transport in thermal QCD
• Thermal conductivity of hot pionic medium due to pion self-energy for $\pi \sigma$ and $\pi \rho$ loops
• Shear viscosity expression for a graphene system in relaxation time approximation
• Transport Coefficients of relativistic matter: A detailed formalism with a gross knowledge of their magnitude
• Possibility of quantum Hall effect in dense quark matter environments: A chiral model approach
• Thermoelectric coefficients of two-flavor quark matter from the Kubo formalism
• Thermoelectric transport coefficients of quark matter