Abstract
We have explored the multi-component structure of electrical conductivity of relativistic Fermionic and Bosonic fluid in presence of magnetic field by using Kubo approach. This is done by explicitly evaluating the thermo-magnetic vector current spectral functions using the real time formalism of finite temperature field theory and the Schwinger proper time formalism. In absence of magnetic field, the one-loop diagramatic representation of Kubo expression of any transport coefficients is exactly same with relaxation time approximation (RTA) based expression, but this equality does not hold for finite magnetic field picture due to lacking of proper implementation of quantum effect in latter approach. We have shown this discrepancy for particular transport coefficient - electrical conductivity, whose starting point in Kubo approach will be electromagnetic current-current correlator and its one-loop skeleton diagram carrying two scalar/Dirac propagators for scalar/Dirac fluid. Through a numerical comparison between RTA and Kubo expressions of conductivity components (parallel and perpendicular), we have attempted to interpret detail quantum field theoretical effect, contained by Kubo expression but not by RTA expression. In classical RTA expression we get magnetic field independent parallel conductivity due to zero Lorentz force but in field theoretical Kubo expression, it decreases and increases with the magnetic field for scalar and Dirac medium respectively due to Landau quantization effect. This parallel component of conductivity can be interpreted as zero momentum limit of quantum fluctuation with same Landau level internal lines. While for perpendicular component of conductivity, fluctuation with Landau level differences $\pm 1$ are noticed, which might be a new realization of transportation in field theoretical sector.
Highlights
Research on quark gluon plasma (QGP), which can be produced in heavy ion collision (HIC) experiment facilities is a mature branch of high energy physics, where a broad band of basic physics from classical mechanics to quantum mechanics to statistical mechanics to quantum field theory are largely cultivated
We will explore the numerical results of Kubo expressions, where we will eventually notice rich information on quantum field theoretical transport properties of a relativistic fluid in the presence of a magnetic field
Realizing an inverse relation between thermal width (Γ) and relaxation time as τc 1⁄4 1=Γ and spin degeneracy factor g 1⁄4 2, 4 for charged scalar and Dirac particles, one can see that relaxation time approximation (RTA) expressions (63) and Kubo expressions
Summary
Research on quark gluon plasma (QGP), which can be produced in heavy ion collision (HIC) experiment facilities is a mature branch of high energy physics, where a broad band of basic physics from classical mechanics to quantum mechanics to statistical mechanics to quantum field theory are largely cultivated As interesting as it is, the creation of very strong magnetic fields of the order 1019–1020 G during noncentral or asymmetric HICs has thrown a plethora of questions requiring a careful study. We adopt the Kubo formlism equipped with Schwinger’s proper time formalism [38,39,40] to calculate electrical conductivity in the presence of an external magnetic field which involves the evaluation of correlation functions [41]. Throughout this paper we use the natural system of units with ħ 1⁄4 c 1⁄4 1 and the metric tensor gμν in flat space given by the signature ðþ; −; −; −Þ
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