how to reduce symmetry

[Neitrino]

Dear PF,

I dont know whether this is the right place for such question, but
how to reduce symmetry suppose from SU(2) symmetric Lagrangian down to U(1)?

Thank you

[Dimitri Terryn]

You can't. If you let the Higgs doublet acquire an VEV in a SU(2) invariant theory, you break the entire SU(2) symmetry and end up with with three massive gauge bosons.

You can however break down SU(2)xU(1) to a (nontrivial) subgroep U(1). This is what is done in the Electroweak theory.

[Neitrino]

Thank you Dimitri