# Defining Integration over SU(3)

• jinbaw
In summary, integration over SU(3) involves calculating the integral of a matrix function over the special unitary group SU(3). This group consists of all 3x3 unitary matrices with determinant 1, and is commonly used in theoretical physics to describe the symmetries of quantum systems. The integration process requires taking into account the group's non-commutative structure and can be achieved through various techniques such as the Haar measure or the Weyl integration formula. Overall, integration over SU(3) is a crucial tool in studying the properties and behaviors of quantum systems with symmetries described by this group.
jinbaw
How is integration over the group SU(3) defined?

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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## 1. What is SU(3)?

SU(3) is a special unitary group of 3x3 complex matrices with determinant equal to 1. It is commonly used in theoretical physics, particularly in the study of quantum chromodynamics.

## 2. Why is Integration over SU(3) important?

Integration over SU(3) is important in the study of quantum chromodynamics and the strong nuclear force as it allows for the calculation of physical observables such as particle masses and decay rates.

## 3. How is Integration over SU(3) performed?

The integration over SU(3) is typically performed using numerical methods or by using analytical techniques such as the Monte Carlo method or the Gaussian quadrature method.

## 4. What are some examples of applications of Integration over SU(3)?

Some examples include the calculation of the strong coupling constant in quantum chromodynamics and the determination of the mass of the Higgs boson in the Standard Model of particle physics.

## 5. Are there any challenges associated with Integration over SU(3)?

Yes, there are several challenges associated with Integration over SU(3), including the complex nature of the integrals and the large number of variables involved. Additionally, the numerical methods used for integration may be computationally intensive and require significant resources.

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