Singular indecomposable representations of sl(2,ℂ) and relativistic wave equations

Bracken A.J. and Cant A. (1989) Singular indecomposable representations of sl(2,ℂ) and relativistic wave equations. Journal of Mathematical Physics, 30 12: 2963-2972. doi:10.1063/1.528484

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Author Bracken A.J.
Cant A.
Title Singular indecomposable representations of sl(2,ℂ) and relativistic wave equations
Journal name Journal of Mathematical Physics   Check publisher's open access policy
ISSN 0022-2488
Publication date 1989-01-01
Sub-type Article (original research)
DOI 10.1063/1.528484
Open Access Status File (Publisher version)
Volume 30
Issue 12
Start page 2963
End page 2972
Total pages 10
Subject 1605 Policy and Administration
Abstract A detailed summary is given of the structure of singular indecomposable representations of si (2,ℂ), as developed by Gel'fand and Ponomarev [Usp. Mat. Nauk 23, 3 (1968); translated in Russ. Math. Surveys 23, 1 (1968)]. A variety of four-vector operators Γμ is constructed, acting within direct sums of such representations, including some with nonsingular Γ0. Associated wave equations of Gel'fand-Yaglom type are considered that admit timelike solutions and lead to mass-spin spectra of the Majorana type. A subclass of these equations is characterized in an invariant way by obtaining basis-independent expressions for the commutator and anticommutator of Γμ and Γν. A brief discussion is given of possible applications to physics of these equations and of others in which nilpotent scalar operators appear.
Q-Index Code C1
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
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