Position-space propagators and a theory of functional fields relevant to the dual-resonance models

Towards the construction of a field theory for dual-resonance models, the Green's functionals for the hadronic "strings" are introduced as natural extensions of the conventional Feynman propagators in position space. To this end, some descriptions on quantum mechanics for a two-dimensional medium along the line of Dirac's action principle are given. The functional propagators assume both Boson and Fermion fields together with the functional equations they satisfy. A rough sketch is attempted of the Lagrangian field theory for the Boson fields; and some schemes of interaction are outlined in terms of the inhomogeneous equations whose elementary solutions are just our propagators. Examples given are the cases in which the general n-point Veneziano amplitude and the amplitudes associated with one-loop diagrams are formally derived.