Abstract
Following Mandelstam's suggestion, we consider a potential which can be expanded in a power series in , beginning with . Then at large energy (positive or negative) there will be Regge poles at all negative integral values of . If the term is absent in the expansion of the potential, the pole at will be absent. Generally, if is the first nonvanishing odd power term in the potential expansion, the poles at are absent. If the potential expansion contains only even non-negative powers of , there will be no Regge poles at finite negative in the limit of large energy. If the potential behaves as at small , the scattering amplitude has a cut in the plane from to , and the Regge poles are no longer located at negative integers at large energy. For finite energy, it is shown that a pole at a positive integer or half-integer implies another pole at but that the residues at these poles are, in general, different from each other.
- Received 27 June 1962
DOI:https://doi.org/10.1103/PhysRev.128.1418
©1962 American Physical Society