The usefulness of QED

QED is often quoted in connection with two of its famous consequences: the Lamb shift and the anomalous magnetic moment of the electron.

The Lamb shift is famous because it was the first calculation that made quantum field theory respectable. The anomalous magnetic moment of the electron is famous because it is the most accurate prediction in physics that we currently have: the agreement with experiment is given up to the 12th significant digit.

But these are only two of a huge number of verifiable consequences of QED, and have no special status beyond the above; indeed, the most useful applications of QED are elsewhere.

Atomic spectroscopy is a consequence of QED, though it can be applied to the standard N-particle Coulomb Hamiltonian (which is the nonrelativistic limit of QED, and thus may be considered not to require QED). But QED is needed if you want to get high accuracy spectra. For heavier elements, it is even needed to get the right order of magnitude. For example, it requires QED to get the color of gold (a spectroscopic property) right. Calculations from the N-particle Coulomb Hamiltonian get the color completely wrong, since important correction terms derived from QED (and incorporated in the Hamiltonian used for relativistic Hartree-Fock calculations, or their more accurate refinements) are missing.

The fact that quicksilver is liquid at room temperature is also a genuine QED effect, as applying the usual statistical mechanics calculations to the N-particle Coulomb Hamiltonian gets the freezing point quite wrong. Again, the Hamiltonian used for the relativistic orbital calculations comes from QED.

One also needs QED in laser-based chemistry, as the interaction between a laser and a molecule cannot be described without QED. Of course, one can work with Hamiltonian approximations, but these involve the concept of a photon and the form of its interactions with the electrons, both borrowed from QED.

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