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Angular analyses in relativistic quantum mechanics; Analyses angulaires en mecanique quantique relativiste

Abstract

This work describes the angular analysis of reactions between particles with spin in a fully relativistic fashion. One particle states are introduced, following Wigner's method, as representations of the inhomogeneous Lorentz group. In order to perform the angular analyses, the reduction of the product of two representations of the inhomogeneous Lorentz group is studied. Clebsch-Gordan coefficients are computed for the following couplings: l-s coupling, helicity coupling, multipolar coupling, and symmetric coupling for more than two particles. Massless and massive particles are handled simultaneously. On the way we construct spinorial amplitudes and free fields; we recall how to establish convergence theorems for angular expansions from analyticity hypothesis. Finally we substitute these hypotheses to the idea of 'potential radius', which gives at low energy the usual 'centrifugal barrier' factors. The presence of such factors had never been deduced from hypotheses compatible with relativistic invariance. (author) [French] On decrit un formalisme permettant de tenir compte de l'invariance relativiste, dans l'analyse angulaire des amplitudes de reaction entre particules de spin quelconque. Suivant Wigner, les etats a une particule sont introduits a l'aide des representations du groupe de Lorentz inhomogene. Pour effectuer les analyses angulaires, on etudie la reduction du produit de deux representations du  More>>
Authors:
Moussa, P [1] 
  1. Commissariat a l'Energie Atomique, 91 - Saclay (France). Centre d'Etudes Nucleaires
Publication Date:
Jun 01, 1968
Product Type:
Thesis/Dissertation
Report Number:
CEA-R-3608
Resource Relation:
Other Information: TH: These Docteur Es-Sciences; 42 refs; PBD: Jun 1968
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CLEBSCH-GORDAN COEFFICIENTS; CONVERGENCE; DIRAC OPERATORS; EIGENVECTORS; FOCK REPRESENTATION; HELICITY; L-S COUPLING; LORENTZ GROUPS; LORENTZ TRANSFORMATIONS; PARITY; QUANTUM MECHANICS; SPIN; WAVE FUNCTIONS; WIGNER THEORY
OSTI ID:
20523391
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France); Faculte des Sciences de l'Universite de Paris, 75 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR04R3608091446
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
[182] pages
Announcement Date:
Dec 10, 2004

Citation Formats

Moussa, P. Angular analyses in relativistic quantum mechanics; Analyses angulaires en mecanique quantique relativiste. France: N. p., 1968. Web.
Moussa, P. Angular analyses in relativistic quantum mechanics; Analyses angulaires en mecanique quantique relativiste. France.
Moussa, P. 1968. "Angular analyses in relativistic quantum mechanics; Analyses angulaires en mecanique quantique relativiste." France.
@misc{etde_20523391,
title = {Angular analyses in relativistic quantum mechanics; Analyses angulaires en mecanique quantique relativiste}
author = {Moussa, P}
abstractNote = {This work describes the angular analysis of reactions between particles with spin in a fully relativistic fashion. One particle states are introduced, following Wigner's method, as representations of the inhomogeneous Lorentz group. In order to perform the angular analyses, the reduction of the product of two representations of the inhomogeneous Lorentz group is studied. Clebsch-Gordan coefficients are computed for the following couplings: l-s coupling, helicity coupling, multipolar coupling, and symmetric coupling for more than two particles. Massless and massive particles are handled simultaneously. On the way we construct spinorial amplitudes and free fields; we recall how to establish convergence theorems for angular expansions from analyticity hypothesis. Finally we substitute these hypotheses to the idea of 'potential radius', which gives at low energy the usual 'centrifugal barrier' factors. The presence of such factors had never been deduced from hypotheses compatible with relativistic invariance. (author) [French] On decrit un formalisme permettant de tenir compte de l'invariance relativiste, dans l'analyse angulaire des amplitudes de reaction entre particules de spin quelconque. Suivant Wigner, les etats a une particule sont introduits a l'aide des representations du groupe de Lorentz inhomogene. Pour effectuer les analyses angulaires, on etudie la reduction du produit de deux representations du groupe de Lorentz inhomogene. Les coefficients de Clebsch-Gordan correspondants sont calcules dans les couplages suivants: couplage l-s couplage d'helicite, couplage multipolaire, couplage symetrique pour plus de deux particules. Les particules de masse nulle et de masse non nulle sont traitees simultanement. Au passage, on introduit les amplitudes spinorielles et on construit les champs libres, on rappelle comment des hypotheses d'analyticite permettent d'etablir des theoremes de convergence pour les developpements angulaires. Enfin on fournit un substitut a la notion de 'portee du potentiel', d'ou resulte la presence a basse energie des facteurs dits 'de barriere centrifuge'. La presence de ces facteurs n'avait jamais ete deduite d'hypotheses compatibles avec l'invariance relativiste. (auteur)}
place = {France}
year = {1968}
month = {Jun}
}