Relativistic Trajectories from a ConfigurationSpace δShell Interaction
Abstract
The Regge spectrum generated by a fourdimensional δshell interaction V(r)=λδ(ra), where r is the fourdimensional radius, is investigated by means of exact solutions of the Wickrotated BetheSalpeter equation. In this model only the leading trajectory can generate resonances. It is infinitely rising with ImαReα<1. Odd daughter trajectories either develop negative imaginary parts or do not rise. Even daughter trajectories turn over above the elastic threshold. This spectrum is contrasted with that obtained from a δshell interaction in potential theory. The potentialtheory model is characterized by an infinite set of parallel, infinitely rising trajectories. The equivalence between the partialwave BetheSalpeter equation and the continuousdimensional formalism used here is explicitly developed. Suggestions are made for extending the method to BetheSalpeter equations involving spin or multichannel effects.
 Publication:

Physical Review D
 Pub Date:
 September 1971
 DOI:
 10.1103/PhysRevD.4.1707
 Bibcode:
 1971PhRvD...4.1707S