We provide a new method to construct the S-matrix in quantum field theory. This method implements crossing symmetry manifestly by erasing the a priori distinction between in- and out-states. It allows the description of processes where the interaction weakens with distance in space, but remains strong in the center at all times. It should also be applicable to certain spacetimes where the conventional method fails due to lack of temporal asymptotic states.

4 pages, LaTeX + revtex4; v2: normalization factors corrected; v3: two paragraphs added, minor corrections and enhancements, reference list updated; v4: references corrected/updated