Wigner-Eckart Theorem: Rigorous Math Treatment

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SUMMARY

The discussion centers on the Wigner-Eckart theorem and the mathematical treatment of Angular Momentum, emphasizing the need for rigorous resources beyond traditional texts like Ballentine. Participants seek materials that approach the subject from the perspective of Lie algebras and groups. A recommended resource is "Symmetries, Lie Algebras and Representations" by Fuchs & Schweigert, which provides a solid mathematical foundation. The focus is on finding comprehensive literature that develops these concepts from the ground up.

PREREQUISITES
  • Understanding of the Wigner-Eckart theorem
  • Familiarity with Angular Momentum in quantum mechanics
  • Knowledge of Lie algebras and groups
  • Basic mathematical rigor in physics
NEXT STEPS
  • Research the Wigner-Eckart theorem in advanced quantum mechanics texts
  • Study Lie algebras and their applications in physics
  • Explore the book "Symmetries, Lie Algebras and Representations" by Fuchs & Schweigert
  • Look for academic papers that provide rigorous treatments of Angular Momentum
USEFUL FOR

Physicists, mathematicians, and students seeking a deeper understanding of quantum mechanics and the mathematical frameworks underlying Angular Momentum and the Wigner-Eckart theorem.

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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