### Abstract

We suggest a new type of kinematical decomposition of the unequal-mass scattering amplitude. We introduce two noncommuting, nondisjunct Poincaré groups, P^{+} and P(^{−}), both of them are subgroups of the P_{1} ⊗P_{2} direct-product group, where P_{1} and P_{2} are the Poincaré groups of the one-particle transformations for the first and the second particle of the two-particle states, respectively. The group P^{+} is identical to the group of the two-particle Poincaré transformations. Our first decomposition for the scattering amplitude is a double expansion with respect to the representations of both the P^{+} and P^{−} groups, simultaneously. The second proposal of ours is the partial-wave analysis not of the centre-of-mass states but of the «equal velocity» states, in which the individual particles move with the same velocity. Our expansions are valid for any s and t. In the equal-mass case they give the usual Lorentz-pole decomposition at t=0. The formalism seems to be adequate for understanding the meaning of the «spectrum generating group» in the unequal-mass case. The variables of the expansion functions are unambiguously defined by the kinematical variables, and have branch points only at the thresholds and pseudothresholds, in opposition to other approaches.

Original language | English |
---|---|

Pages (from-to) | 371-400 |

Number of pages | 30 |

Journal | Il Nuovo Cimento A Series 11 |

Volume | 66 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1970 |

### Fingerprint

### ASJC Scopus subject areas

- Astronomy and Astrophysics
- Nuclear and High Energy Physics
- Atomic and Molecular Physics, and Optics

### Cite this

*Il Nuovo Cimento A Series 11*,

*66*(2), 371-400. https://doi.org/10.1007/BF02824792

**On the introduction of Lorentz poles into the unequal-mass scattering amplitude.** / Szegö, K.; Tóth, K.

Research output: Contribution to journal › Article

*Il Nuovo Cimento A Series 11*, vol. 66, no. 2, pp. 371-400. https://doi.org/10.1007/BF02824792

}

TY - JOUR

T1 - On the introduction of Lorentz poles into the unequal-mass scattering amplitude

AU - Szegö, K.

AU - Tóth, K.

PY - 1970

Y1 - 1970

N2 - We suggest a new type of kinematical decomposition of the unequal-mass scattering amplitude. We introduce two noncommuting, nondisjunct Poincaré groups, P+ and P(−), both of them are subgroups of the P1 ⊗P2 direct-product group, where P1 and P2 are the Poincaré groups of the one-particle transformations for the first and the second particle of the two-particle states, respectively. The group P+ is identical to the group of the two-particle Poincaré transformations. Our first decomposition for the scattering amplitude is a double expansion with respect to the representations of both the P+ and P− groups, simultaneously. The second proposal of ours is the partial-wave analysis not of the centre-of-mass states but of the «equal velocity» states, in which the individual particles move with the same velocity. Our expansions are valid for any s and t. In the equal-mass case they give the usual Lorentz-pole decomposition at t=0. The formalism seems to be adequate for understanding the meaning of the «spectrum generating group» in the unequal-mass case. The variables of the expansion functions are unambiguously defined by the kinematical variables, and have branch points only at the thresholds and pseudothresholds, in opposition to other approaches.

AB - We suggest a new type of kinematical decomposition of the unequal-mass scattering amplitude. We introduce two noncommuting, nondisjunct Poincaré groups, P+ and P(−), both of them are subgroups of the P1 ⊗P2 direct-product group, where P1 and P2 are the Poincaré groups of the one-particle transformations for the first and the second particle of the two-particle states, respectively. The group P+ is identical to the group of the two-particle Poincaré transformations. Our first decomposition for the scattering amplitude is a double expansion with respect to the representations of both the P+ and P− groups, simultaneously. The second proposal of ours is the partial-wave analysis not of the centre-of-mass states but of the «equal velocity» states, in which the individual particles move with the same velocity. Our expansions are valid for any s and t. In the equal-mass case they give the usual Lorentz-pole decomposition at t=0. The formalism seems to be adequate for understanding the meaning of the «spectrum generating group» in the unequal-mass case. The variables of the expansion functions are unambiguously defined by the kinematical variables, and have branch points only at the thresholds and pseudothresholds, in opposition to other approaches.

UR - http://www.scopus.com/inward/record.url?scp=84951181745&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84951181745&partnerID=8YFLogxK

U2 - 10.1007/BF02824792

DO - 10.1007/BF02824792

M3 - Article

AN - SCOPUS:84951181745

VL - 66

SP - 371

EP - 400

JO - Il Nuovo Cimento A Series 11

JF - Il Nuovo Cimento A Series 11

SN - 0369-3546

IS - 2

ER -