Scattering of one-dimensional bags in the interacting string formalism
Charles B. Thorn, Martin V. K. Úlehla
Abstract
Charles B. Thorn, Martin V. K. Úlehla
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 ${(\mathrm{mass})}^{2}$, $\ensuremath{-}4\ensuremath{\pi}B{\ensuremath{\alpha}}_{0}$, of the ground state be $\ensuremath{-}4\ensuremath{\pi}B$. 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 ${\ensuremath{\alpha}}_{0}$. Then these still possess crossing symmetry but are not Lorentz covariant unless ${\ensuremath{\alpha}}_{0}=1$.
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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 ${(\mathrm{mass})}^{2}$, $\ensuremath{-}4\ensuremath{\pi}B{\ensuremath{\alpha}}_{0}$, of the ground state be $\ensuremath{-}4\ensuremath{\pi}B$. 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 ${\ensuremath{\alpha}}_{0}$. Then these still possess crossing symmetry but are not Lorentz covariant unless ${\ensuremath{\alpha}}_{0}=1$.
Key concepts: Physics, Crossing, Scattering amplitude, Scattering, Formalism (music), Covariant transformation, Lorentz transformation, Mathematical physics