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S9e. QED and relativistic quantum chemistry
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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