Quantum field theoretical structure of electrical conductivity of cold and dense fermionic matter in the presence of a magnetic field

Abstract

We have gone through a detailed calculation of the two-point correlation function of vector currents at finite density and magnetic field by employing the real time formalism of finite temperature field theory and Schwinger's proper time formalism. With respect to the direction of external magnetic field, the parallel and perpendicular components of electric conductivity for the degenerate relativistic fermionic matter are obtained from the zero momentum limit of the current-current correlator, owing to Kubo formula. Our quantum field theoretical expressions and numerical estimations are compared with the same, obtained from the relaxation time approximation methods of kinetic theory and its Landau quantized extension, which may be called as classical and quantum results respectively. All the results are merged in the classical domain i.e. high density and low magnetic field region but in the remaining (quantum) domain, quantum results carry a quantized information like Shubnikov-de Haas oscillation along density and magnetic field axes. We have obtained completely new quantum field theoretical expression for perpendicular conductivity of degenerate relativistic fermionic matter. Interestingly, our quantum field theoretical calculation provide a new mathematical form of cyclotron frequency with respect to its classical definition, which might require more future research to interpret the phenomena.

arXiv commentVersion published in Physical Review D

References in corpus (46)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Physics of Strongly Magnetized Neutron Stars
• From hadrons to quarks in neutron stars: a review
• Evidence for quark-matter cores in massive neutron stars
• "Strongly interacting matter in magnetic fields": an overview
• Hydrodynamic Transport Coefficients in Relativistic Scalar Field Theory
• General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests
• Gravitational and electromagnetic outputs from binary neutron star mergers
• Kubo formulas for relativistic fluids in strong magnetic fields
• General-relativistic resistive-magnetohydrodynamic simulations of binary neutron stars
• Electrical Conductivity of Quark-Gluon Plasma in Strong Magnetic Fields
• The electrical conductivity of a pion gas
• Longitudinal Conductivity in Strong Magnetic Field in Perturbative QCD: Complete Leading Order
• The weak-field expansion for processes in a homogeneous background magnetic field
• QED effective action at finite temperature and density
• Electric conductivity of hot and dense quark matter in a magnetic field with Landau level resummation via kinetic equations
• Effective potential at finite temperature in a constant magnetic field I: Ring diagrams in a scalar theory
• Effective description of hot QCD medium in strong magnetic field and longitudinal conductivity
• Electrical conductivity of a warm neutron star crust in magnetic fields
• Anisotropic transport properties of Hadron Resonance Gas in magnetic field
• Transport coefficients of hot magnetized QCD matter beyond the lowest Landau level approximation
• Linking electromagnetic and gravitational radiation in coalescing binary neutron stars
• Real-Time Thermal Propagators and the QED Effective Action for an External Magnetic Field
• Electrical conductivity and Hall conductivity of hot and dense hadron gas in a magnetic field: a relaxation time approach
• Transport coefficients of hot and dense hadron gas in a magnetic field: a relaxation time approach
• Electrical conductivity and Hall conductivity of hot and dense quark gluon plasma in a magnetic field: a quasi particle approach
• Anisotropic electrical conductivity of magnetized hot quark matter
• Electrical conductivity of quark matter at finite T under external magnetic field
• Shear viscosity of pion gas due to $\rho \pi \pi$ and $\sigma \pi \pi$ interactions
• Electrical Conductivity of Dense Quark Matter with Fluctuations and Magnetic Field Included
• Kubo estimation of the electrical conductivity for a hot relativistic fluid in the presence of a magnetic field
• Real-time propagators at finite temperature and chemical potential
• Electrical Resistivity and Hall Effect in Binary Neutron-Star Mergers
• Resummation for the Field-theoretical Derivation of the Negative Magnetoresistance
• Thermal Field Theory in real-time formalism: concepts and applications for particle decays
• Mass modification of hot pions in magnetized dense medium
• Morphology and characteristics of radio pulsars
• Phenomenological bound on the viscosity of the hadron resonance gas
• Medium effects on the electrical conductivity of a hot pion gas
• In-medium viscous coefficients of a hot hadronic gas mixture
• Proper-Time Formalism in a Constant Magnetic Field at Finite Temperature and Chemical Potential
• Chiral fermion mass and dispersion relations at finite temperature in the presence of hypermagnetic fields
• Effect of magnetized phonons on electrical and thermal conductivity of neutron star crust
• Propagators of charged particles in an external magnetic field, expanded over Landau levels
• Contribution of Kaon component in viscosity and conductivity of hadronic medium
• Scattering cross-section under external magnetic field using the optical theorem