Infrared-Finite Algorithms in QED for Ground States and Scattering Matrix Elements

For a nonrelativistic atom coupled to the quantized radiation field, an algorithm for the construction of the ground state, the ground energy, and (Rayleigh) scattering matrix elements is derived. The algorithm allows to expand these quantities in explicit form in terms of bare quantities, to arbitrary accuracy, in powers of the finestructure constant $\alpha$. This is joint work with J. Fröhlich and A. Pizzo.