A mandelstam representation in potential scattering

Field Theories with Persistent One Particle States. I. General Formalism

“…(a/ai)Q-'(t)lo) = (a/at)ln(t) ) = 0 (23) Thus in the present theory there is neither vacuum polarization nor are there self-energy effectsa vacuum stays a vacuumand a one-particle state remains a one-particle state. It is no doubt obvious that this is just the purpose of the persistence assurnptions.…”

“…(d) There are now several proofs of the validity of the Mandelstam representation in potential scattering, provided that the potentials satisfy certain regularity conditions (Elein [21]; Blankenbecler, Goldberger, Ehuri, and Treiman [22]; and Bowcock and Martin [23]). Although these proofs are of great interest, they refer to potential scattering only.…”

Physics in the CERN Theory Division

“…His initial programme on the analyticity domain aimed at proving the entire Mandelstam representation from the axioms of field theory. Already in 1959 he gave, in collaboration with John Bowcock, a first derivation in the framework of a potential model [22]. In 1966 he obtained the first results in relativistic field theory.…”

Physical Meaning of Redundant Poles ofS-Matrix

“…For fixed t, the scattering amplitudes are regular 2 ) as func-tions of s except for the cuts in the positive real axis and the poles corresponding to the bound states. Each term of the perturbation expansion of the scattering amplitude satisfies 3 ) the Mandelstam representation. Now, when we want to discuss the analytic properties of the scattering amplitude, p. in (1) corresponds to the mass of the exchanged pion.…”

“…The singularities at (12) can be verified by the direct calculation. 3 ) The partial wave amplitude is singular only when the scattering amplitude for cos8=±1 is singular. Therefore, the redundant singularities (5) are nothing but the ones due to the singularities (12).…”