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

[Anne-Sylvie]

Hello everyone,

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, which 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. :-)

 

[Avodyne]

See chapters 83, 88, and 89 in the book by Srednicki (draft version freely downloadable at his web page).

 

[Anne-Sylvie]

Thanks for your advice. :-)