Abstract
The meaning of Castillejo-Dalitz-Dyson poles (CDD poles) in the field-theoretic context of a boson separable-potential model is studied. Because the asymptotic-field operators for this model depend upon the function, it is possible to insert CDD poles into these fields and to gauge their effect. It is found that CDD poles have a profound influence: Their presence prevents the in-fields from satisfying canonical commutation relations. A return to the free-particle algebra is possible, however, if new particles are inserted into the theory, one for every pole. These new particles are unstable, thus confirming the link between CDD poles and instability. A further consequence of this work is the development of a method for constructing Hamiltonians which, a priori, yield scattering amplitudes containing CDD poles.
- Received 20 February 1967
DOI:https://doi.org/10.1103/PhysRev.160.1428
©1967 American Physical Society