Spin‐weighted cylindrical harmonics and the Euclidean group of the plane

It is shown that the spin‐weighted cylindrical harmonics s  J αm (ρ,φ), which are functions defined on the plane, are related to representation matrices of the group of rigid motions on the plane. It is also shown that the raising and lowering operators of the spin weight and of the z component of t...

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Bibliographic Details
Published in:Journal of mathematical physics 1993-08, Vol.34 (8), p.3856-3862
Main Author: Torres del Castillo, G. F.
Format: Article
Language:English
Subjects:
Algebraic methods
Classical and quantum physics: mechanics and fields
Exact sciences and technology
Physics
Quantum mechanics
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Summary:It is shown that the spin‐weighted cylindrical harmonics s  J αm (ρ,φ), which are functions defined on the plane, are related to representation matrices of the group of rigid motions on the plane. It is also shown that the raising and lowering operators of the spin weight and of the z component of the angular momentum are related to two copies of the Lie algebra of the Euclidean group of the plane.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.530011