Is there any general method to construct the generators of a SU(n) group?
what do you mean "construct"? do you mean "find representation of"? if so, then the answer is "yes!": you can find all the reps of the compact semisimple Lie groups using the method of highest weights. any compact Lie group has a discrete set of representations, which of course is why quantum numbers are quantum, instead of continuous.
Can you tell me what mathematical model you would use to represent cooper pairing in superconductors? I.e. you need a model of spin, and you need a model of spin pairing. What physical model/lie group configuration can explain this? Does it need to be relativistic?
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