The projective Lie algebra of the Lorentz group and homographic transformations

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1978 English Publisher:AIP PublishingJournal:Journal of Mathematical Physics, volume 19, pages 1,196-1,197 (issn: 0022-2488, eissn: 1089-7658,

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Authors: Bacry, H.;

doi: 10.1063/1.523784

The projective Lie algebra of the Lorentz group and homographic transformations

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Abstract

The Lorentz group is used as the group of homographic transformations on the Riemann sphere. Its Lie algebra is shown to have a very simple interpretation with the aid of cross products and constellation formalism. This property is used to give a constellation description of the Clebsch–Gordan series for the product of two states of spin 1.

Related Organizations

French National Centre for Scientific Research
France
Centre de Physique Théorique
France

Keywords

Structure and representation of the Lorentz group, Applications of Lie groups to the sciences; explicit representations, Lie algebras of Lie groups

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