Forward Scattering Amplitude and Univalent Functions
Abstract
Starting with the relativistic crossingsymmetric forward scattering amplitude, we constructed previously a function g(E) of energy E which is both analytic and univalent (schlicht) in the upperhalf energy plane. In this paper we exploit the univalence of g(E) to obtain information on the analytic properties of the forwardscattering amplitude. Various inequalities satisfied by g(E) are derived, making use of powerful theorems on univalent functions. In particular, we have established several theorems which relate the asymptotic behavior of the phase of g(E) to that of g(E) itself. We have also obtained several inequalities for g(E) which may be useful in an experimental test of the consequences of local field theory. We start with only those properties of the forward scattering amplitude that have already been proved in axiomatic local field theory. The only extra assumption used that has not yet been proved in field theory is the physical assumption that the forward scattering amplitude does not become relatively real in the highenergy limit.
 Publication:

Physical Review
 Pub Date:
 November 1965
 DOI:
 10.1103/PhysRev.140.B706
 Bibcode:
 1965PhRv..140..706K