Infrared-finite algorithms in QED:: The groundstate of an atom interacting with the quantized radiation field

In this paper, the groundstate of a nonrelativistic atom, minimally coupled to the quantized radiation field, and its groundstate energy are constructed by an iteration scheme inspired by [10]. This scheme successively removes an infrared cutoff in momentum space and yields a convergent algorithm enabling us to calculate the groundstate and the groundstate energy, to arbitrary order in the feinstructure constant alpha similar to 1/137. In forthcoming papers, we will use our result to re-expand the groundstate and, eventually, scattering amplitudes in terms of bare quantities.