It turns out it is important to include *positron Dirac sea* into the relativistic (meaning starting from the Dirac equation) description of how Rydberg electrons respond to weak optical fields.

Yes, positrons were invented to avoid the collapse of electrons into the continuum of states below the rest-mass gap and that brilliant speculation led to the entire idea of experimentally-observed antimatter. And, yes, Rydberg electrons are non-relativistic (in fact, nearly classical) so why would they know about antimatter? Is not it surprising? What we find is that in certain gauges one would fail to recover even the leading order of the AC Stark effect without including antimatter. Here is the link to the full paper, which has other goodies as well.

**Dynamic polarizability of Rydberg atoms: applicability of the near-free-electron approximation, gauge invariance, and the Dirac sea**, T. Topcu and A. Derevianko, *Phys. Rev. A 88, 042510 (2013)**, http://arxiv.org/abs/1308.0573*

*Abstract:* Ponderomotive energy shifts experienced by Rydberg atoms in optical fields are known to be well approximated by the classical quiver energy of a free electron. We examine such energy shifts quantum mechanically and elucidate how they relate to the ponderomotive shift of a free electron in off-resonant fields. We derive and evaluate corrections to the ponderomotive free-electron polarizability in the length and velocity (transverse or Coulomb) gauges, which agree exactly as mandated by the gauge invariance. We also show how the free electron value emerges from the Dirac equation through summation over the Dirac sea states. We find that the free-electron ac Stark shift comes as an expectation value of a term proportional to the square of the vector potential in the velocity gauge. On the other hand, the same dominant contribution can be obtained to first order via a series expansion of the exact energy shift from the second-order perturbation theory in the length gauge. Finally, we numerically examine the validity of the free-electron approximation. The correction to the free-electron value becomes smaller with increasing principal quantum number, and it is well below a percent for 60*s* states of Rb and Sr away from the resonances.