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Spectral and scattering theory at low energy for the relativisticSchroedinger operator are investigated. Some striking properties at thresholdsof this operator are exhibited, as for example the absence of 0-energyresonance. Low energy behavior of the wave operators and of the scatteringoperator are studied, and stationary expressions in terms of generalizedeigenfunctions are proved for the former operators. Under slightly strongerconditions on the perturbation the absolute continuity of the spectrum on thepositive semi axis is demonstrated. Finally, an explicit formula for the actionof the free evolution group is derived. Such a formula, which is well known inthe usual Schroedinger case, was apparently not available in the relativisticsetting.

Low energy spectral and scattering theory for relativistic Schroedinger operators