Matrices of su(3) and sphere symmetry

In summary, matrices are essential in the study of su(3) and sphere symmetry as they represent the transformation of these mathematical structures and simplify complex calculations. In su(3), matrices are used to describe symmetry operators, while in other types of symmetry, they are crucial in understanding and analyzing symmetries. In physics, matrices of su(3) and sphere symmetry are used to describe physical systems and can lead to new discoveries. The applications of these matrices are diverse, ranging from fundamental physics to practical fields such as data analysis and cryptography.
  • #1
kimcj
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i used to get pauli matrices by the following steps
it uses the symmetry of a complex plane sphere i guess so..?
however i can't get the 8 gell mann matrices
please help !

method*: (x y) * (a b / c d ) = (x' y')
use |x|^2 + |y|^2 = |x'|^2 + |y'|^2
and |x| = x * x(complex conjugate)

this way i can get 3 pauli matrices
however can't apply them to su(3) ones..
 
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  • #2
The Pauli matrices are elements of ##SU(2)## and span ##\mathfrak{su}(2)##. A (random) coincidence.

The Gell-Mann matrices are not elements of ##SU(3)##. They span ##\mathfrak{su}(3)##.
 
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Related to Matrices of su(3) and sphere symmetry

1. What is the significance of matrices in the study of su(3) and sphere symmetry?

Matrices play a crucial role in the study of su(3) and sphere symmetry, as they are used to represent the transformation of these mathematical structures. By using matrices, we can simplify complex calculations and better understand the properties and behavior of su(3) and sphere symmetry.

2. How do matrices relate to the concept of symmetry in su(3)?

In su(3), matrices are used to represent the symmetry operators that preserve the structure of the system. These operators act on the elements of the system, such as particles or fields, and transform them while maintaining the same overall structure. Matrices are essential in describing the symmetries of su(3) and understanding their implications.

3. Can matrices be used to study other types of symmetry besides sphere symmetry?

Yes, matrices can be used to study various types of symmetry, including rotational, translational, and reflection symmetries. They are a powerful tool in understanding and analyzing symmetries in different mathematical structures, such as groups, Lie algebras, and manifolds.

4. How are matrices of su(3) and sphere symmetry related to physical systems?

Matrices of su(3) and sphere symmetry are often used in physics to describe the symmetries of physical systems. These matrices can represent the transformation of particles, states, and fields in a physical system, providing insights into its behavior and properties. The study of these matrices can also lead to the discovery of new physical laws and phenomena.

5. What are the applications of matrices of su(3) and sphere symmetry in real-world scenarios?

The applications of matrices of su(3) and sphere symmetry are vast and diverse. They are used in fields such as quantum mechanics, particle physics, and condensed matter physics to describe fundamental symmetries and their implications. They are also used in data analysis, cryptography, and computer graphics to solve complex problems and improve efficiency.

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