Leading Order Calculation of Electric Conductivity in Hot Quantum Electrodynamics from Diagrammatic Methods

Abstract

Using diagrammatic methods, we show how the Ward identity can be used to constrain the ladder kernel in transport coefficient calculations. More specifically, we use the Ward identity to determine the necessary diagrams that must be resummed using an integral equation. One of our main results is an equation relating the kernel of the integral equation with functional derivatives of the full self-energy; it is similar to what is obtained with 2PI effective action methods. However, since we use the Ward identity as our starting point, gauge invariance is preserved. Using power counting arguments, we also show which self-energies must be included in the resummation at leading order, including 2 to 2 scatterings and 1 to 2 collinear scatterings with the LPM effect. We show that our quantum field theory result is equivalent to the one of Arnold, Moore and Yaffe obtained using effective kinetic theory. In this paper we restrict our discussion to electrical conductivity in hot QED, but our method can in principle be generalized to other transport coefficients and other theories.

45 pages, 16 figures. Typos corrected, some explanations added to power counting, some clarifications added in various places

References in corpus (1)

• The Bulk Viscosity of High-Temperature QCD

Cited by in corpus (39)

• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• Second order hydrodynamic coefficients from kinetic theory
• Perturbative Thermal QCD: Formalism and Applications
• Shear and bulk viscosities of the gluon plasma in a quasiparticle description
• Electrical Conductivity of Quark-Gluon Plasma in Strong Magnetic Fields
• Leading Order Calculation of Shear Viscosity in Hot Quantum Electrodynamics from Diagrammatic Methods
• Bulk Viscosity of Quark-Gluon Plasma in Strong Magnetic Fields
• Quasiparticle Theory of Transport Coefficients for Hadronic Matter at Finite Temperature and Baryon Density
• Chiral electric separation effect in the quark-gluon plasma
• Small shear viscosity in the semi quark gluon plasma
• Bulk Viscosity of a Gas of Massless Pions
• Bulk Viscosity at Extreme Limits: From Kinetic Theory to Strings
• Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics
• Gluon Spectrum in Quark-Gluon Plasma under Strong Magnetic Fields
• Kubo formulae for the shear and bulk viscosity relaxation times and the scalar field theory shear ${\tau }_{\pi }$ calculation
• On the Role of Quasiparticles and thermal Masses in Nonequilibrium Processes in a Plasma
• Leading Order QED Electrical Conductivity from the 3PI Effective Action
• QED Electrical Conductivity using the 2PI Effective Action
• Ultrasoft Fermionic Modes at High Temperature
• Leading Order QCD Shear Viscosity from the 3PI Effective Action
• Renormalized Linear Kinetic Theory as Derived from Quantum Field Theory - a novel diagrammatic method for computing transport coefficients -
• Second Order Transport Coefficient from Chiral Anomaly at Weak Coupling: Diagrammatic Resummation
• Next-to-Leading Order Shear Viscosity in lambda phi^4 Theory
• Hadronic transport coefficients from the linear sigma model at finite temperature
• Ultra-soft fermionic excitation at finite chemical potential
• Spectral Function of Fermion Coupled with Massive Vector Boson at Finite Temperature in Gauge Invariant Formalism
• Ultrasoft fermion mode and off-diagonal Boltzmann equation in quark-gluon plasma at high temperature
• Systematics of High Temperature Perturbation Theory: The Two-Loop Electron Self-Energy in QED
• Dense Quark Matter Conductivity in Ultra-Intense Magnetic Field
• Off-diagonal kinetic theory in ultrasoft momentum region at high temperature
• The noncommutativity of the static and homogeneous limit of the axial chemical potential in chiral magnetic effect
• Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green-Kubo Method within the 2-flavour gauged NJL model
• Analytical formulas for shear and bulk viscosities in relativistic gaseous mixtures with constant cross sections
• Relativistic Heavy Ion Collisions: Viscous Hydrodynamic Simulations and Final State Interactions
• Viscosities of the quasigluon plasma
• In-medium Electromagnetic Form Factors and Spin Polarizations
• Review of heat and charge transport in strongly magnetized relativistic plasmas
• The shear and bulk relaxation times from the general correlation functions
• Electrical conductivity of hot Abelian plasma with scalar charge carriers