Scattering of one-dimensional bags in the interacting string formalism

Abstract

We apply the interacting string formalism of Mandelstam to the scattering problem of one-dimensional bags. Lorentz covariance together with general properties of the path-integral formalism require that the number of constituent fields be 24 and that the ${\mathrm{}\left(\mathrm{mass}\right)\mathrm{}}^2$, $-4\mathrm{}\pi B{\alpha }_0$, of the ground state be $-4\mathrm{}\pi B$. In this case, the $n$-point scattering amplitudes are precisely those of the dual resonance model. However, we also write the four-point scattering amplitudes for arbitrary ${\alpha }_0$. Then these still possess crossing symmetry but are not Lorentz covariant unless ${\alpha }_0=1\mathrm{}$.