Abstract
We study the electrical conductivity of hot Abelian plasma containing scalar charge carriers in the leading logarithmic order in coupling constant $\alpha$ using the Boltzmann kinetic equation. The leading contribution to the collision integral is due to the M{\o}ller and Bhabha scattering of scalar particles with a singular cross section in the region of small momentum transfer. Regularizing this singularity by taking into account the hard thermal loop corrections to the propagators of intermediate particles, we derive the second order differential equation which determines the kinetic function. We solve this equation numerically and also use a variational approach in order to find a simple analytical formula for the conductivity. It has the standard parametric dependence on the coupling constant $\sigma\approx 2.38\, T/(\alpha \log\alpha^{-1})$ with the prefactor taking a somewhat lower value compared to the fermionic case. Finally, we consider the general case of hot Abelian plasma with an arbitrary number of scalar and fermionic particle species and derive the simple analytical formula for its conductivity.
Highlights
Transport coefficients are very important characteristics of any medium providing information about its response to external perturbations
We study the electrical conductivity of hot Abelian plasma containing scalar charge carriers in the leading logarithmic order in coupling constant α using the Boltzmann kinetic equation
We studied the electrical conductivity of a general hot Abelian plasma with ultrarelativistic scalar and fermionic charge carriers in the framework of kinetic theory
Summary
Transport coefficients are very important characteristics of any medium providing information about its response to external perturbations. Correlation functions of the conserved currents in the low momentum and frequency limit (the so-called Kubo relations) These correlators have to be calculated in finite temperature quantum field theory and the leading order result is obtained by the resummation of an infinite number of ladder diagrams. [42,43,44,45,46,47,48,49], the electric conductivity of such a plasma was calculated by the variety of methods, including Kubo relations, kinetic approach, chiral perturbation theory etc. In the Appendix we provide some details of the calculation of the collision integral in the leading-log order
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