Singlets and Doublets in SU(2)

[ryanwilk]

Hi, this is probably very simple.

1) What is the product of two singlets?
2) What is the product of two singlets and a doublet?

It looks like (2) breaks SU(2) symmetry and (1) doesn't, but I don't really understand why =/.

Any help would be appreciated,

Thanks!

 

[ofirg]

Any representation remains the same when taking a product of it and a singlet


1) A singlet

2) A doublet

any non singlet which has a non zero expectation value in the vacuum of the theory breaks the SU(2) symmetry.