Can Quarks Form a Basis for SU(2) Using Only the I3 Space?

In summary, the u, d, and s quarks can represent the basis of a 3x3 representation of SU(2) when looking at the ##I_3## space, as the SU(2) group is isomorphic to a subgroup of SU(3).
  • #1
Silviu
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Hello! I am reading something related to algebra in particle physics and I want to make sure I got it. So, they say the u, d and s quarks can represent the basis of the SU(3) representation when the diagonalizable matrices are Y=B+S and ##I_3##. But, if I want to look only in the ##I_3## space (without Y), can I say that u, d and s represent the basis of a 3x3 representation of SU(2)?
Thank you!
 
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  • #2


Hello there! That is a great question. Yes, you are correct in saying that u, d, and s quarks can represent the basis of a 3x3 representation of SU(2) when looking only at the ##I_3## space. This is because the SU(2) group is isomorphic to a subgroup of SU(3), meaning that the same mathematical structure exists in both groups. In other words, the u, d, and s quarks can be seen as a subset of the larger SU(3) representation when looking at just the ##I_3## space. Keep up the good work in your studies of algebra in particle physics!
 

FAQ: Can Quarks Form a Basis for SU(2) Using Only the I3 Space?

1. What is SU(2) and SU(3) of quarks?

SU(2) and SU(3) are mathematical groups that describe the internal symmetries of elementary particles, specifically quarks. SU(2) represents the symmetries of spin-1/2 particles, while SU(3) represents the symmetries of color charge in quarks.

2. How do SU(2) and SU(3) relate to the Standard Model of particle physics?

SU(2) and SU(3) are fundamental building blocks of the Standard Model, which is the most widely accepted theory describing the behavior of subatomic particles. The SU(2) group is a key component of the electroweak force, while SU(3) is a fundamental symmetry of the strong nuclear force.

3. What is the significance of the number 2 and 3 in SU(2) and SU(3)?

The numbers 2 and 3 refer to the dimensionality of the mathematical group. In SU(2), the group has two dimensions, representing the two possible spin states of particles. In SU(3), the group has three dimensions, representing the three possible colors of quarks.

4. How do SU(2) and SU(3) affect the properties of quarks?

The symmetries described by SU(2) and SU(3) play a crucial role in determining the properties and interactions of quarks. For example, the SU(3) symmetry of color charge allows for the existence of eight different types of quarks, known as flavors. Additionally, the SU(2) symmetry of spin dictates that quarks have a spin of 1/2.

5. Are there other mathematical groups that are relevant to quarks?

Yes, there are other mathematical groups that play a role in the description of quarks and other elementary particles. For example, the SU(5) and SO(10) groups have been proposed as potential unification theories that could explain the relationship between the strong, weak, and electromagnetic forces. The study of mathematical groups and their application to particle physics is an ongoing area of research.

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