How is Integration over SU(3) Defined?

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    Integration Su(3)
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SUMMARY

Integration over the group SU(3) is defined using the Haar Measure, which serves as the invariant volume element necessary for integration on compact Lie groups. A relevant reference for understanding this concept is the document available at Haar Measure PDF. Additionally, the discussion highlights the similarity between integrating over SU(2) and the sphere S^3, suggesting that a similar framework applies to SU(3). For a comprehensive understanding, the document at this link is recommended, particularly section 4, which covers Euler-angle parametrization and the definition of the invariant volume element.

PREREQUISITES
  • Understanding of Haar Measure in the context of Lie groups
  • Familiarity with compact Lie groups, specifically SU(2) and SU(3)
  • Knowledge of Euler-angle parametrization techniques
  • Basic concepts of integration on manifolds
NEXT STEPS
  • Study the properties of Haar Measure in detail
  • Explore the integration techniques on compact Lie groups
  • Learn about the generators of SU(3) and their significance
  • Investigate the applications of SU(3) in quantum mechanics and particle physics
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Mathematicians, physicists, and researchers interested in advanced topics in group theory, particularly those focusing on integration over Lie groups and their applications in theoretical physics.

jinbaw
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How is integration over the group SU(3) defined?
 
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The keyword is: Haar Measure. See for example this http://gemma.ujf.cas.cz/~brauner/files/Haar_measure.pdf" .

Sorry for the short answer, I'm in a hurry.
 
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I passed over a discussion which shows that integrating over SU(2) is similar to that over a sphere S^3. I want a similar discussion for integration over SU(3).
Can someone please specify a reference that gives a good explanation of SU(3) (like finding generators, etc..)?
Thanks
 

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