Expansions of the unequal-mass scattering amplitude in terms of poincaré representations and complex angular momentum at zero energy

K. Szegö, K. Tóth

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The expansion of the unequal-mass scattering amplitude in terms of Poincaré-group representations was considered for positive and zero values of s, the squared total four-momentum. The usual singularity problem at s=0 was avoidable, but it turned out that the relevant variable is not j, the total angular momentum, but a quantity nonsingularly related to the Poincaré-invariant WμWμ even at s=0. The notion of complex angular momentum and signature was reexamined, and some modification of the old formalism seemed useful. The results are perfectly compatible with dispersion relations and with the requirements of Regge behavior. In an appendix a theorem is proved for the expansion of a class of functions which are not square-integrable, but have Regge behavior with respect to unitary E(2) representations (that is, for Fourier-Bessel expansions).

Original languageEnglish
Pages (from-to)1297-1307
Number of pages11
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume5
Issue number6
DOIs
Publication statusPublished - 1972

Fingerprint

scattering amplitude
angular momentum
expansion
energy
theorems
signatures
formalism
momentum
requirements

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

@article{3e2cf87e9dd645a5ab873254fd98e17e,
title = "Expansions of the unequal-mass scattering amplitude in terms of poincar{\'e} representations and complex angular momentum at zero energy",
abstract = "The expansion of the unequal-mass scattering amplitude in terms of Poincar{\'e}-group representations was considered for positive and zero values of s, the squared total four-momentum. The usual singularity problem at s=0 was avoidable, but it turned out that the relevant variable is not j, the total angular momentum, but a quantity nonsingularly related to the Poincar{\'e}-invariant WμWμ even at s=0. The notion of complex angular momentum and signature was reexamined, and some modification of the old formalism seemed useful. The results are perfectly compatible with dispersion relations and with the requirements of Regge behavior. In an appendix a theorem is proved for the expansion of a class of functions which are not square-integrable, but have Regge behavior with respect to unitary E(2) representations (that is, for Fourier-Bessel expansions).",
author = "K. Szeg{\"o} and K. T{\'o}th",
year = "1972",
doi = "10.1103/PhysRevD.5.1297",
language = "English",
volume = "5",
pages = "1297--1307",
journal = "Physical review D: Particles and fields",
issn = "1550-7998",
publisher = "American Institute of Physics Publising LLC",
number = "6",

}

TY - JOUR

T1 - Expansions of the unequal-mass scattering amplitude in terms of poincaré representations and complex angular momentum at zero energy

AU - Szegö, K.

AU - Tóth, K.

PY - 1972

Y1 - 1972

N2 - The expansion of the unequal-mass scattering amplitude in terms of Poincaré-group representations was considered for positive and zero values of s, the squared total four-momentum. The usual singularity problem at s=0 was avoidable, but it turned out that the relevant variable is not j, the total angular momentum, but a quantity nonsingularly related to the Poincaré-invariant WμWμ even at s=0. The notion of complex angular momentum and signature was reexamined, and some modification of the old formalism seemed useful. The results are perfectly compatible with dispersion relations and with the requirements of Regge behavior. In an appendix a theorem is proved for the expansion of a class of functions which are not square-integrable, but have Regge behavior with respect to unitary E(2) representations (that is, for Fourier-Bessel expansions).

AB - The expansion of the unequal-mass scattering amplitude in terms of Poincaré-group representations was considered for positive and zero values of s, the squared total four-momentum. The usual singularity problem at s=0 was avoidable, but it turned out that the relevant variable is not j, the total angular momentum, but a quantity nonsingularly related to the Poincaré-invariant WμWμ even at s=0. The notion of complex angular momentum and signature was reexamined, and some modification of the old formalism seemed useful. The results are perfectly compatible with dispersion relations and with the requirements of Regge behavior. In an appendix a theorem is proved for the expansion of a class of functions which are not square-integrable, but have Regge behavior with respect to unitary E(2) representations (that is, for Fourier-Bessel expansions).

UR - http://www.scopus.com/inward/record.url?scp=35949027144&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949027144&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.5.1297

DO - 10.1103/PhysRevD.5.1297

M3 - Article

AN - SCOPUS:35949027144

VL - 5

SP - 1297

EP - 1307

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 6

ER -