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Rotation matrices corresponding to complex angular momenta

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Il Nuovo Cimento (1955-1965)

Summary

We try to extend to complex values of the angular momentum the idea of a representation of the rotation groupR 3. Using the homeomorphism between the unitary unimodular groupU 2 andR 3, we build a set of infinite matrices, each one singular at one pole of the sphere; they give back the usual rotation matrices for integer or half-integer values of the angular momentum. The product rules of these matrices are discussed, and the resulting structure is analysed: it retains some but not all the properties of a group representation.

Riassunto

StudiÄmo una estensione del concetto di rappresentazione del gruppo delle rotazioniR 3 nel caso di valori complessi del momento angolare caratteristico della rappresentazione stessa. Utilizzando l’omeomornsmo esistente fra il gruppo unitario unimodulareU 2 edR 3 si costmisce esplicitamente un insieme di matrici infinite, ognuna delle quali presenta singolarità in un polo della sfera. Per valori interi o seminteri del momento angolare esse restituiscono le usuali matrici di rotazione. Si studiano le proprietá di moltiplicazione di tali matrici e la struttura del loro insieme, la quale mantiene alcune, ma non tutte, le proprietà gruppali.

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References

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Authors and Affiliations

  1. Istituto di Fisioa dell’ Université, Genova

    E. G. Beltrametti & G. Luzzatto

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Genova, Italy

    E. G. Beltrametti & G. Luzzatto

Authors
  1. E. G. Beltrametti
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  2. G. Luzzatto
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Beltrametti, E.G., Luzzatto, G. Rotation matrices corresponding to complex angular momenta. Nuovo Cim 29, 1003–1018 (1963). https://doi.org/10.1007/BF02750126

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  • DOI: https://doi.org/10.1007/BF02750126

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