Foundations of the Relativistic Theory of Many-Electron systems

A hamiltonian with linear kinetic energy for systems of many bodies

“…The approach cannot give a proper treatm ent of nuclear properties and hyperfine interactions, nor does it include annihilation forces between electrons and positrons as in positronium, nor does it incorporate quantum electrodynamics, although th a t could be put into the potential. Finally, nothing has been said about the negative energies entailed by the relativistic form of the ham iltonian; the m atter has been extensively discussed since the work of Brown & Ravenhall (1951) (see Sucher 1983); here it is tacitly assumed th a t a solution can be found to the problem. I thank Professor Abdus Salam, F.R.S., the International Atomic Energy Agency and UNESCO for hospitality at the International Centre for Theoretical Physics, Trieste.…”

“…In much of the work just mentioned, attention has been concentrated on the interactions between particles and on the problem of states of negative energy (for a review see Sucher 1983), and the form of the kinetic energy operator seems to have been written down almost without discussion with the exception of Kemmer (I 937)-Thus, generally, the kinetic energy of a system of many electrons around a nucleus of infinite mass has been taken to be just the sum of the kinetic energies (in Dirac form) of the individual electrons. W ith th a t approxim ation, it is not possible to include the reduced-mass effect of the motion of the nucleus (but see B arut & Komy 1985), and th a t is satisfactory for atom s w ith m any electrons, in which the electron-electron interactions are far more im portant than the effects of the motions of nuclei with finite mass.…”

Spectral problems about many-body Dirac operators mentioned by Dereziński

“…These problems were originally formulated by B. Jeziorski who is a chemist from the University of Warsaw (cf. J. Sucher [10] p.6). Among them there are spectral problems on Dirac-Coulomb operator H DC for a helium-like ion, which has the form…”

All-order relativistic computations for atoms and molecules using an explicitly correlated Gaussian basis

“…Sucher proposed [25][26][27][28] a no-pair many-particle Hamiltonian based on relativistic QED that is reminiscent to the naïvely constructed Hamiltonian in Eq. ( 1) with the important difference that it is projected with Λ + to the positive energy states (E + ) of a non-interacting reference problem, H 0 = n i=1 (h i + u i ):…”

“…Sucher explains [25][26][27][28] that H 0 can be either the kinetic energy of the free spin-1/2 fermions or some other bound model without fermion-fermion interactions following Furry's work [29]. This no-pair operator, in some cases called the Brown-Ravenhall operator [30], has well-defined mathematical properties, and most importantly, it is bounded from below.…”