Wigner-Eckart Theorem: Rigorous Math Treatment

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Discussion Overview

The discussion centers on seeking rigorous mathematical treatments of the Wigner-Eckart theorem and angular momentum, particularly from the perspective of Lie algebras and groups. Participants are looking for resources that provide a deeper mathematical foundation than traditional texts.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant expresses a need for more rigorous material on the Wigner-Eckart theorem and angular momentum, specifically seeking resources that cover the topic from a foundational mathematical perspective.
  • Another participant inquires about the specific type of rigor being sought.
  • A participant specifies that they are interested in treatments from the viewpoint of Lie algebras and groups, ideally starting from the basics.
  • A suggestion is made to consider the book "Symmetries, Lie Algebras and Representations" by Fuchs & Schweigert as a good mathematical resource.
  • A later reply acknowledges the suggestion and expresses intent to explore the recommended material.

Areas of Agreement / Disagreement

Participants appear to agree on the need for more rigorous resources, but there is no consensus on specific materials beyond the suggestion made.

Contextual Notes

The discussion does not clarify the specific aspects of rigor desired, nor does it resolve the broader question of which resources are most suitable for this level of mathematical treatment.

Who May Find This Useful

Readers interested in advanced mathematical treatments of quantum mechanics, particularly those focusing on angular momentum and representation theory.

WiFO215
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I originally posted this in the Science Book and discussion forum but received no help. Am posting it here, hoping that I will.

I was looking for material that would go over the Wigner Eckart theorem and mathematics of Angular Momentum in more rigor than the traditional texts do (in specific Ballentine). I am not only looking for books, but any papers, articles which treat the following in a more rigorous mathematical footing would be appreciated.
 
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What kind of rigor are you looking for?
 
From the point of view of Lie algebras and groups. Hopefully, one that develops the material from scratch.
 
For a mathematical treatment of this kind of thing, I have found Fuchs & Schweigert "Symmetries, Lie Algebras and Representations" good.
 
Thanks henry. I'll look into it.
 

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