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