I am trying to learn about the various SU groups related to QCD. I have about 5 QFT and Particle physics books from my student library and written down about 20 pages of handwritten notes about specific parts of say generators, matrices, group properties etc. - but i dont really feel that I understand the deeper connection between all this. Can someone (preferably) in simple words and not too many equations, explain what relevant SU symmetries connect QCD and HOW?(adsbygoogle = window.adsbygoogle || []).push({});

To me it seems impossible to get a feeling of the big picture here. I feel that when i zoom in on a specific part it gets somewhat clear, but i need to understand the bigger picture. I am specifically interested in the connection between chiral symmetry - the left/right-handedness breakdown to vector/axial symmetry - what is happening here? I can understand that this can be done in SU(2) handeling only u and d quarks - or SU(3) handeling u, d, and s quarks. One is a better approximation than the other - again why?

How does this relate to the 8 Goldstone bosons (3 pions, 3 kaons, 2 eta) emerging when going from SU(3)_L x SU(3)_R to only SU(3)_V

The same can be said for the SU(2) "version" of this, where the breakdown gives rise to 3 Goldstone bosons (the 3 pions). I know that theory says they need to be massless, but how do we then use it as a legit model strong interactions?

i have read on the linear sigma model, eightfold way, chiral symmetry transformations, rotational transformations, gauge invariance among many things. What i really want is to connect some of the ideas. I know i am asking an extremely broad question, so feel free to choose any smaller domain you would like :-)

Thank you very much!

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# A SU groups in QCD

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