I was reading this thread on "representation and field theory" under(adsbygoogle = window.adsbygoogle || []).push({});

physics > quatnum physics

https://www.physicsforums.com/showthread.php?t=91764

which got me thinking...and perhaps there are experts out there who can clarify these for me:

(A.1) In particle physics we often speak of something as being a singlet, doublet, triplet...etc. in SU(3), SU(2) or the5in SU(5)... or whatever. What do they actually mean?

(A.2) eg. we put leptons into doublets, typically in a 2x1 vector... so I guess we are assuming the 2x2 matrix representation of SU(2)? My question is does thedimensionalityof the vector space/tensor/representation (not sure which one I should be talking about) got anything to do with whether we call something a singlet, doublet, triplet... etc?

OR

does the fact that there are "two"(or three or one) items to be juggled with dictate whether something is called a "doublet" (or triplet or singlet) respectively?

(A.3) Related to this is the issue of irreducibility of tensors/representations. Do we always choose irreducible rep for putting in our particle contents? ie. say in SU(3), there are1,3,6,8irreducible reps etc, does that mean one cannot have a SU(3) doublet (there is no2rep)? If not, how can this be written down?

(A.4) finally, when we introduce the Higgs doublet to create a mass term which is invariant under the group action, I noticed that in that context, we often say that we need a doublet Higgs because 2x2=1+3 contains a singlet! So are we now talking about combining two reps in such a way that we end up not having juggled anything? Or is there anything deeper than that? Doesn't a direct product of 2 and 2 give us a "bigger" space? or only the irreducible bit (related to A.3) matters?

I've got a feeling that I may have mixed up a lot of concenpts (irreducible representations, irreducible tensors, representation space, dim of rep and dim of matrix...etc.), pls feel free to correct me where applicable. Thanks in advance.

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# What are doublets, singletsin SU(N)?

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