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When we speak about the SU(2)L group (in electroweak interactions for example), about what group do we talk ? What is the difference with the SU(2) group ? And with the SU(2)R ? Why is the label so important ?

I ask this because I see that a Lagrangien can be invariant under SU(2)L x SU(2)R. I think that means that if we apply any transformation of the SU(2)L and then SU(2)R on the lagrangien, it will give the same lagrangien as before. Is it right ?

Then, when we consider the Higgs mechanism. There is an non zero expectation value, and then via the spontaneous symmetry breaking mechanism, a higgs field appear, etc, and we have another lagrangien. This lagrangien is no longer invariant under SU(2)L x SU(2)R transformations, but well under SU(2)L+R. What does that mean ? What is SU(2)L+R ? How can we know, when we spontaneously break a symmetry, wich symmetries will survive ?

I'm a bit confused with all of that. I hope I'm relatively clear in my message... Please excuse me for my English but I'm non native and I'm still learning this usefull langage. :-)

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# SU(2)L, SU(2)R, other symmetric groups and SSB

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