Correspondence and Analyticity

Abstract

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 singularity surfaces, and the analytic character (e.g., pole, logarithmic, etc.) of these singularities. These important properties of the S-matrix are thus derived without using stringent locality assumptions, or the Schrödinger equation for temporal evolution, except for freely moving particles. Sum-over-all-paths methods that emphasize paths of stationary action tend to produce the quantum analogs of the contributions from classical paths. These quantum analogs are derived directly from the associated classical properties by reverse engineering the correspondence-principle connection.