Duality and Internal Space-Time Structure of Hadrons. I

Abstract

The Veneziano amplitude is analyzed as a consequence of a propagation of an extended object. The so-called duality is explained in this scheme to mean an equivalence between the propagation effects of the extended object through the direct channel and the crossed channel. The internal degrees of freedom and the interaction structure of the extended object required from the above duality are clarified. A single (4+2)-dimensional relativistic harmonic oscillator is needed as an internal degree of freedom. The interaction Hamiltonian of extended objects with such an internal structure is obtained, which leads us to the Veneziano amplitude of two-body reaction and enables us to get any amplitudes for higher order inelastic processes. The result is compared with the so-called generalized n-point dual amplitude, which is known to require for its dynamical derivation an infinite number of (5-dimensional) relativistic harmonic oscillators as internal degrees of freedom.