Derivation of the Kelbg potential/functional

TL;DR

This paper derives the Kelbg potential from the Coulomb interaction in the high-temperature limit, clarifying the derivation process to facilitate its application in path integral simulations of Coulomb systems.

Contribution

It provides a detailed derivation of the Kelbg potential using the Bloch equation, enhancing understanding of this important tool in Coulomb system simulations.

Findings

Derivation of the Kelbg potential in the high-temperature limit

Simplified explanation of the transformations involved

Potential application in path integral simulations

Abstract

The density matrix for a system of particles interacting via the Coulomb potential is obtained in the high--temperature limit following almost entirely the original work by Kelbg. For this purpose the Bl\"och equation is solved in the first order of perturbation theory. We tried to explain all the transformations in the derivation in order to simplify the understanding of this non-trivial theory. The solution of Kelbg is widely used in path integral simulations of Coulomb systems.