It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms (see e.g. http://ncatlab.org/nlab/show/FQFT). I.e. to any (spacelike) hypersurface in the target we associate a ...