# Electrical conductivity of hot Abelian plasma with scalar charge carriers

## TL;DR

This paper calculates the electrical conductivity of a hot Abelian plasma with scalar charge carriers, using kinetic theory and numerical methods, revealing a standard dependence on the coupling constant with a specific prefactor.

## Contribution

It provides the first detailed calculation of conductivity in scalar-charge Abelian plasma, including regularization of singular cross sections and an analytical formula applicable to multiple particle species.

## Key findings

- Conductivity scales as approximately 2.38 T / (α log(1/α))
- Derived a simple analytical formula for plasma conductivity
- Extended results to arbitrary numbers of scalar and fermionic species

## 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.