Holomorphy of the scattering matrix with respect to c-2 for Dirac operators and an explicit treatment of relativistic corrections

We prove holomorphy of the scattering matrix at fixed energy with respect to c-2 for abstract Dirac operators. Relativistic corrections of order c-2 to the nonrelativistic limit scattering matrix (associated with an abstract Pauli Hamiltonian) are explicitly determined. As applications of our abstract approach we discuss concrete realizations of the Dirac operator in one and three dimensions and explicitly compute relativistic corrections of order c-2 of the reflection and transmission coefficients in one dimension and of the scattering matrix in three dimensions. Moreover, we give a comparison between our approach and the first-order relativistic corrections according to Foldy-Wouthuysen scattering theory and show complete agreement of the two methods. (orig.)