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## Main Question or Discussion Point

This is my (limited) understanding of particle physics: In particle physics gauge symmetries play an important role. To allow for massive gauge bosons this symmetry is broken. The theory of weak interactions can be derived from a local SU(2) symmetry, and quantumchromodynamics from a local SU(3) symmetry.

I read the structures particles form when sorted by certain quantum numbers can be described by groups too. Eg Y/Tz diagrams baryon plots. What have these structures got to do with the SU(3) groups? As I understand it elements of SU(3) can be written as:

[tex]U=exp(i \sum_{k=1} ^{k=8} a_k t_k)[/tex]

With the generators [itex] t_k [/tex] the Gell-Mann matrices eg. I see the number 8, and also the 3 as in the number of quarks in a baryon, also appearing in the partical structures but can't see the connection between them and this piece of mathematics.

So my questions are:

1)how do these particle structures realte to the mathematics of group theory? (note that my knowledge of group theory is very limited)

2) Has the symmetry breaking in gauge theories have anything to do with the broken symmetries (eg the masses of the particles in the multplets differ, the symmetries are not complete) in particle multiplets?

I read the structures particles form when sorted by certain quantum numbers can be described by groups too. Eg Y/Tz diagrams baryon plots. What have these structures got to do with the SU(3) groups? As I understand it elements of SU(3) can be written as:

[tex]U=exp(i \sum_{k=1} ^{k=8} a_k t_k)[/tex]

With the generators [itex] t_k [/tex] the Gell-Mann matrices eg. I see the number 8, and also the 3 as in the number of quarks in a baryon, also appearing in the partical structures but can't see the connection between them and this piece of mathematics.

So my questions are:

1)how do these particle structures realte to the mathematics of group theory? (note that my knowledge of group theory is very limited)

2) Has the symmetry breaking in gauge theories have anything to do with the broken symmetries (eg the masses of the particles in the multplets differ, the symmetries are not complete) in particle multiplets?

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