Density and pair-density scaling for deriving the Euler equation in density-functional and pair-density-functional theory

A link between density and pair density functional theories is presented. Density and pair density scaling are used to derive the Euler equation in both theories. Density scaling provides a constructive way of obtaining approximations for the Pauli potential. The Pauli potential (energy) of the density functional theory is expressed as the difference of the scaled and original exchange-correlation potentials (energies).