A formulation of quantum electrodynamics is given that applies to atoms in astrong laser field by perturbation theory in a non-relativistic regime. Dipoleapproximation is assumed. The dual Dyson series, here discussed by referring itto the Birkhoff theorem for singularly perturbed linear differential equations,can be applied and a perturbation series obtained transforming the Hamiltonianby a Pauli-Fierz transformation. But, if just few photons are presenthigh-order harmonics cannot be generated. So, it is proven that odd high-orderharmonics only appear when the laser field is intense and one can substitutethe creation and annihilation operators by the square root of the mean numberof photons taken to be huge, the field retaining its coherency property asobserved experimentally for harmonics. In this case, the Hamiltonian forperturbation theory comes to the Kramers-Henneberger form. The theory has adipolar contribution when the free-electron quiver motion amplitude is largerthan the atomic radius. For a Coulomb potential one has that the outer electronis periodically kicked, and so a prove is given that the same should happen toRydberg atoms in intense microwave fields. The distribution representing thekicking has a Fourier series with just odd terms. Using a modifiedRayleigh-Schr\"odinger perturbation theory, it is shown that under the samecondition of validity of the quiver motion amplitude to atomic radius ratio,the atomic wave function is only slightly modified by the laser field due tothe way the energy levels rearrange themselves. This gives a prove ofstabilization in the limit of laser frequency going to infinity. Then,perturbation theory can be applied when the Keldysh parameter becomes smallerwith respect to the shifted distance between the energy levels of the atom.
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