Systematic derivation of the Kelbg functional and pseudopotential
In this paper the density matrix for a system of particles interacting via the Coulomb potential is systematically derived in the high-temperature limit. The derivation corresponds to the original work by Kelbg [\href{https://doi.org/10.1002/andp.19634670308}{Kelbg G 1963 Annalen der Physik \textbf{467} 219-224}], which solves the Bl\"och equation in the first order of perturbation theory. Special attention is paid 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.