IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v114y1982i1p28-49.html
   My bibliography  Save this article

The overlap concept of Clebsch-Gordan coefficients and Racah lemma constants

Author

Listed:
  • Schäffer, Claus E.

Abstract

By virtue of the isomorphic relationship between simple tensor products |l1t1〉|l2t2〉, formed from othonormal bases of real functions, and the corresponding operators Ŝl1t1l2t2 = |l1t1〉〈l2t2| obtains analogous overlap expressions (scalar products) for functions and operators when using the trace definition of operator overlap. Defining R3-irreducible tensorial quantities [|l1{⊗}l2|]l3t3 (for functions) and [|l1{ ⊗ }l2|]l3t3 (for operators) by the same expansion formulae, one makes Clebsch-Gordan coefficients expressible as function overlaps of the type 〈l1t1|〉l2t2|[|l1{ ⊗ |l2{]l3t3 and as operator overlaps of the type 〈Ŝl1t1l2t2|[|l1{ ⊗ }l2|]l3t3〉. Similarly, Racah lemma constants (isoscalar factors) obtain overlap interpretations.

Suggested Citation

  • Schäffer, Claus E., 1982. "The overlap concept of Clebsch-Gordan coefficients and Racah lemma constants," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 114(1), pages 28-49.
    • Handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:28-49
    DOI: 10.1016/0378-4371(82)90257-6
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437182902576
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(82)90257-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yudson, V.I., 1990. "Covariant approach to the wilson renormalization of nonlinear σ models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 167(1), pages 140-148.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:114:y:1982:i:1:p:28-49. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.