Correspondence and analyticity

The analyticity properties of the S matrix in the physical region are determined by the correspondence principle, which asserts that the predictions of classical physics are generated by taking the classical limit of the predictions of quantum theory. The analyticity properties deducible in this way from classical properties include the locations of the singularity surfaces, the rules for analytic continuation around these surfaces, and the analytic character (e.g., pole, logarithmic, etc.) of these singulatities. These important properties of the S matrix are thus derived without using stringent locality assumptions. The quantum properties are derived by an analytic reverse engineering of the classical properties.