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Scattering of one-dimensional bags in the interacting string formalism

Charles B. Thorn, Martin V. K. Úlehla

Open publisher page 4 citations

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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What this paper is about

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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Available 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 ${\ensuremath{\alpha}}_{0}=1$.

Key concepts: Physics, Crossing, Scattering amplitude, Scattering, Formalism (music), Covariant transformation, Lorentz transformation, Mathematical physics

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