Properties of Lorentz Covariant Analytic Functions

A theorem is proved that asserts, roughly, that a function that is real Lorentz covariant anywhere is complex Lorentz covariant everywhere in its domain of regularity. It is also shown that the analytic continuation of a scattering function from a regularity domain in the physical region of a given process along all paths generated by complex Lorentz transformations leads to a function that is single-valued in the neighborhood of all these paths. Applications are discussed. The results derived constitute necessary preliminaries to a discussion of the analytic structure of scattering functions given in other papers.