Generalizations of dual models

Abstract

Generalizations of the dual model are discussed in the context of functional integral formulation of the theory. We notice that all the symmetries of dual amplitudes are led from the symmetries of the Lagrangian used for the measure of functional integration. Irreducible fields under conformal transformations are classified by their dimension and conformal spin. Since the factorizability of dual amplitudes requires a local Langrarian, we construct the general form of local Langrarian density such that the action integral is conformal invariant. We found that if one restricts the form of the Langrangian to bilinear form of the fields, the kinetic term of the Langrarian is possible to construct only for conformal spin 0 and 1 2 field. The former yields the usual dual model, while the latter yields the Bardakçi-Halpern model and the Neveu-Schwarz one. Quantization of conformal spin 1 2 field is discussed in detail. The generating functional of this field is constructed in terms of the functional integral technique and used to construct the general N-particle amplitudes.