Finding a Parametrization for SU(3) in Terms of Angles

Thread starter yola
Start date Jan 31, 2011
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Parametrization Su(3)

In summary, SU(3) is a special unitary group in three dimensions used in quantum mechanics to describe the symmetry of systems with three quantum states. It can be parametrized using various approaches, making it easier to analyze and understand its behavior. SU(3) is crucial in the quark model and has applications in other areas of physics such as nuclear and particle physics.

Jan 31, 2011

yola

How can we find a parametrization for SU(3) in terms of angles?

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Feb 3, 2011

fzero

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You might take a look at http://arxiv.org/abs/physics/9708015

1. What is SU(3) in the context of parametrization?

SU(3) is a special unitary group in three dimensions, which is a mathematical concept used in quantum mechanics to describe the symmetry of a system with three quantum states. In the context of parametrization, SU(3) refers to the process of representing elements of this group using a set of parameters.

2. Why is parametrization important in SU(3)?

Parametrization allows us to simplify the mathematical calculations involved in working with SU(3) by expressing its elements in terms of a smaller set of variables. This makes it easier to analyze and understand the behavior of systems described by SU(3) and can lead to new insights and discoveries.

3. How is SU(3) parametrized?

SU(3) can be parametrized using several different approaches, including the Cartan decomposition, the polar decomposition, and the Balian-Bloch parametrization. Each of these methods involves expressing elements of SU(3) in terms of a specific set of parameters, which can be chosen based on the particular application or problem being studied.

4. What is the relationship between SU(3) and the quark model?

SU(3) plays a crucial role in the quark model, which is a theoretical framework used to describe the interactions between subatomic particles called quarks. In this model, the properties of quarks (such as their mass and charge) are related to the elements of SU(3) through a process known as symmetry breaking.

5. How does SU(3) parametrization relate to other areas of physics?

SU(3) is not only relevant in the field of quantum mechanics, but also has applications in other areas of physics such as nuclear and particle physics. For example, the SU(3) symmetry is used to classify different types of hadrons (particles made up of quarks) and to predict their properties. Additionally, SU(3) parametrization has connections to topics like gauge theories and string theory.