Generating functions in dual models
P. M. Vervoort · Radboud Repository (Radboud University) · 1975
I Operator formalism equivalent to the forms already mentioned.This formalism makes the factorization properties of the amplitude obvious and moreover presents an elegant way to describe the spectrum of the intermediate states in terms of a Fock space of occupation number states, built from a vacuum with simple creation operators.Their operator formalism was strongly connected with the SL(2, R) transformation group which already dominated the Koba-Nielsen form, Although the model even in its Born approximation still suffered from the presence of ghosts (intermediate states with the wrong coupling to the other particles) one started to complete the model with higher order terms in order to restore the unitarity which a single Born term is lacking.This unitarization program has never been completed.Instead, one found a way to eliminate all ghosts by enlarging Sb{2, R) as symmetry group to the set of all conformai transformations in the complex plane which transform the real axis into itself with conservation of the sense of direction.The restrictions of these transformations to the real axis form a group.To make this extension possible the mass of the external scalar particles had to be fixed at an unphysical value; the result was a model containing tachyons, but a ghostfree one.We will refer to this model as the Classical Veneziano model (C.V.M.).The operator formalism in itself opened new paths to other models.The method should not be considered as a lucky coincidence, it can be used as a direct way of construction.The first to use it were A. Neveu and J.H. Schwarz [Ne 71 ] , who after one attempt [He 71 ] succeeded in the construction of a model with a much more realistic although still not physical spectrum• After this Heveu-Schwarz model (N.5.M.) a lot of models were constructed all in the same way [ Ba 71, CI 71 a, , Ha 71] .Ramond even found [ Ra 71] the formalism for a spectrum of fermions.This model was later used to build a fermion-fermion amplitude [Al 73, Sch 73 , Co 73] although