Non-local correlation and point transformations in density functional theory

The present day importance of density functional theory stems from the fact that it attempts to bypass the usual treatment of a quantum mechanical many-body problem based on Schroedinger's equation and to replace it by another one whose fundamental mathematical entity is the one-particle density /rho/ (/rvec/r1). Obviously, since /rho/ (/rvec/r1) depends, regardless of the size of the physical system, only upon 3 spatial coordinates, such an undertaking, if successful, would bring considerable simplifications to the many body problem. The authors discuss some recent results concerning the non-local kinetic energy term. They show that this non-local term is a basic ingredient of density functional theory and, in particular, they indicate how this also applies to the exact differential equation for /rho/ (r)/sup 1/2/ recently advanced by Levy, Perdew and Sahni. Finally, they briefly discuss the use of point transformations for the representation of the non-local correlation function