What is the Haar Measure on SO(4) and Where Can I Find References?

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SUMMARY

The discussion focuses on the Haar measure on SO(4), specifically seeking an explicit expression in terms of angles or the Lebesgue integral over a subset of the Lie algebra. A reference provided is the appendix of the paper found at arxiv.org/abs/0805.0267, which contains relevant information despite a noted typo. The conversation emphasizes the importance of accurate mathematical expressions in understanding the Haar measure.

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  • Understanding of Haar measures in the context of Lie groups
  • Familiarity with SO(4) and its properties
  • Knowledge of Lebesgue integrals and their applications
  • Basic concepts of Lie algebras
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  • Research the properties of Haar measures on compact Lie groups
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  • Examine the specific paper at arxiv.org/abs/0805.0267 for detailed methodologies
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Bobhawke
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I wasn't quite sure where to post this question, so please forgive me if I chose the wrong place.

Essentially I'm looking for an explicit expression for the Haar measure on SO(4), i.e. in terms of angles, or if you prefer, expressed in terms of the Lebesgue integral over a subset of the Lie algebra.

Does anyone know any references which might contain this?

Thank you.
 
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Bobhawke said:
I wasn't quite sure where to post this question, so please forgive me if I chose the wrong place.

Essentially I'm looking for an explicit expression for the Haar measure on SO(4), i.e. in terms of angles, or if you prefer, expressed in terms of the Lebesgue integral over a subset of the Lie algebra.

Does anyone know any references which might contain this?

Thank you.

There's one in the appendix of http://arxiv.org/abs/0805.0267. There is at least one typo there, but the overall construction is using the correct methods.
 
Thank you!
 

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