Swift, Arthur R. and Tucker, Robin
(1971)
*Relativistic trajectories from a configuration-space δ -shell interaction.*
Physical Review D, 4 (6).
pp. 1707-1716.
ISSN 1550-7998

## Abstract

The Regge spectrum generated by a four-dimensional δ -shell interaction V(r)=λδ(r−a) , where r is the four-dimensional radius, is investigated by means of exact solutions of the Wick-rotated Bethe-Salpeter 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 δ -shell interaction in potential theory. The potential-theory model is characterized by an infinite set of parallel, infinitely rising trajectories. The equivalence between the partial-wave Bethe-Salpeter equation and the continuous-dimensional formalism used here is explicitly developed. Suggestions are made for extending the method to Bethe-Salpeter equations involving spin or multichannel effects.