Applications of the reggeon calculus to dual models

The reggeon calculus devised by Polkinghorne to study the j-plane structure of hybrid graphs is utilised to investigate the orientable non-planar dual loop. A hybrid model with quark vertices is also studied and the calculus extended to deal with a dual reggeon triangle graph which contributes to the asymptotic behaviour of a simple production process. Finally the results from single dual loops are expressed in terms of a reggeon operator calculus