The relativistic many body problem in molecular theory

The essential features of current methods to take care of correlation effects in non-relativistic calculations are reviewed, with special attention to configuration interaction (CI) and coupled cluster (CC) methods. It is stressed that most of these methods start from a Fock space Hamiltonian. Then relativistic many-electron Hamiltonians are discussed, especially concerning their accuracy, problems related to the definition of electronic and positronic states and to variational collapse. Special attention is given to `no-pair' Hamiltonians, as well as to various choices of the electron interaction. After some comments on the adaptation of standard methods for electron correlation to the relativistic case, the state of the art of molecular relativistic many-electron theory is described. In an appendix a semiclassical derivation of a relativistic many-electron Hamiltonian is outlined.