Spectral and scattering theory at low energy for the relativistic
Schroedinger operator are investigated. Some striking properties at thresholds
of this operator are exhibited, as for example the absence of 0-energy
resonance. Low energy behavior of the wave operators and of the scattering
operator are studied, and stationary expressions in terms of generalized
eigenfunctions are proved for the former operators. Under slightly stronger
conditions on the perturbation the absolute continuity of the spectrum on the
positive semi axis is demonstrated. Finally, an explicit formula for the action
of the free evolution group is derived. Such a formula, which is well known in
the usual Schroedinger case, was apparently not available in the relativistic
setting.Comment: 27 page