### Abstract

This work is a first step in a program for construction of meson-meson scattering amplitudes with analyticity, crossing symmetry, and unitarity. The construction is to be carried out by solving a nonlinear integral equation for the partial wave amplitude a(l, s) at complex l and physical s. The program is intended to overcome the difficulties encountered in the traditional approach based on the Mandelstam iteration of double-spectral functions. An important initial step is to analyze nonrelativistic potential scattering from this autonomous S-matrix viewpoint, in which the Schrödinger equation is replaced by a nonlinear equation for the partial wave amplitude. In the present paper, it is demonstrated that the partial-wave equation has a locally unique solution, provided the potential is of a suitably restricted Yukawa type. This result indicates the feasibility of a pure S-matrix approach to dynamics. In the present report, the potential is so restricted in strength as to preclude bound states or resonances. The extension of the method to the case of strong potentials will be pursued in a later publication.

Original language | English |
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Pages (from-to) | 1886-1900 |

Number of pages | 15 |

Journal | Journal of Mathematical Physics |

Volume | 16 |

Issue number | 9 |

Publication status | Published - 1974 |

Externally published | Yes |

### Cite this

*Journal of Mathematical Physics*,

*16*(9), 1886-1900.

}

*Journal of Mathematical Physics*, vol. 16, no. 9, pp. 1886-1900.

**Regge amplitudes through solution of S-matrix equations.** / Frederiksen, Jørgen S.; Johnson, Porter W.; Warnock, Robert L.

Research output: Contribution to journal › Article › Other

TY - JOUR

T1 - Regge amplitudes through solution of S-matrix equations

AU - Frederiksen, Jørgen S.

AU - Johnson, Porter W.

AU - Warnock, Robert L.

PY - 1974

Y1 - 1974

N2 - This work is a first step in a program for construction of meson-meson scattering amplitudes with analyticity, crossing symmetry, and unitarity. The construction is to be carried out by solving a nonlinear integral equation for the partial wave amplitude a(l, s) at complex l and physical s. The program is intended to overcome the difficulties encountered in the traditional approach based on the Mandelstam iteration of double-spectral functions. An important initial step is to analyze nonrelativistic potential scattering from this autonomous S-matrix viewpoint, in which the Schrödinger equation is replaced by a nonlinear equation for the partial wave amplitude. In the present paper, it is demonstrated that the partial-wave equation has a locally unique solution, provided the potential is of a suitably restricted Yukawa type. This result indicates the feasibility of a pure S-matrix approach to dynamics. In the present report, the potential is so restricted in strength as to preclude bound states or resonances. The extension of the method to the case of strong potentials will be pursued in a later publication.

AB - This work is a first step in a program for construction of meson-meson scattering amplitudes with analyticity, crossing symmetry, and unitarity. The construction is to be carried out by solving a nonlinear integral equation for the partial wave amplitude a(l, s) at complex l and physical s. The program is intended to overcome the difficulties encountered in the traditional approach based on the Mandelstam iteration of double-spectral functions. An important initial step is to analyze nonrelativistic potential scattering from this autonomous S-matrix viewpoint, in which the Schrödinger equation is replaced by a nonlinear equation for the partial wave amplitude. In the present paper, it is demonstrated that the partial-wave equation has a locally unique solution, provided the potential is of a suitably restricted Yukawa type. This result indicates the feasibility of a pure S-matrix approach to dynamics. In the present report, the potential is so restricted in strength as to preclude bound states or resonances. The extension of the method to the case of strong potentials will be pursued in a later publication.

UR - http://www.scopus.com/inward/record.url?scp=36749108170&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 1886

EP - 1900

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 9

ER -