QED and relativistic quantum chemistry

Relativistic quantum chemistry is needed to predict properties
of heavy atoms. This is usually done by invoking the Dirac-Fock
Hamiltonian, which is an approximation of the QED Hamiltonian
for which the multiparticle bound state problem is tractable.

Here are a few samples of what can be done:
The first is explicitly time-dependent;
the second is about bound states calculations;
the third shows how to add further QED corrections;
The fourth shows how the Dirac-Fock Hamiltonian arises as
approximation of QED. The last gives a discussion of some
mathematical problems involved.

Fink+Johnson
Electron correlations and spin-orbit interaction in two-photon
ionization of closed-shell atoms: A relativistic time-dependent
Dirac-Fock approach
Phys. Rev. A 42, 3801-3818 (1990)
Bieron et al.
Large-scale multiconfigurational Dirac-Fock calculations of the
hyperfine-structure constants and determination of the nuclear
quadrupole moment of 49Ti
Phys. Rev. A 59, 4295-4299 (1999)
Indelicato+Desclaux
Multiconfiguration Dirac-Fock calculations of transition energies
with QED corrections in three-electron ions
Phys. Rev. A 42, 5139-5149 (1990)
P Chaix and D Iracane
From quantum electrodynamics to mean-field theory.
I. The Bogoliubov-Dirac-Fock formalism
J. Phys. B: At. Mol. Opt. Phys. 22 (1989) 3791-3814
M Defranceschi and C Le Bris
Computing a molecule in its environment: A mathematical viewpoint
Int J Quantum Chemistry 71 (1999) 227-250

A recent article by

Werner Kutzelnigg,
Solved and unsolved problems in relativistic quantum chemistry,
Chemical Physics 395 (2012), 16-34.

describes what the title promises. One cannot calculate well many
things of interest. A prime example is the Helium fine structure; cf.
Ingvar Lindgren,
The helium fine-structure controversy
arxiv paper

Anyone who wants to understand the complexity of QED calculations should
read these articles and perhaps leaf through the book

Ingvar Lindgren
Relativistic Many-Body Theory: A New Field-Theoretical Approach,
Springer 2011.
online copy

Arnold Neumaier (Arnold.Neumaier@univie.ac.at)
A theoretical physics FAQ