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