wormwoodsilver101
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- What are the continuous global symmetries before and after the spontaneous symmetry breaking of doublet of scalar fields? And what is the proof for the symmetry?
What are the global symmetries before and after symmetry breaking?
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The global symmetries of a Lagrangian DON’T change “after the spontaneous symmetry breaking”. The Lagrangian you wrote is invariant under the global U(1) transformation [itex]\phi \to e^{i \theta} \phi[/itex]. It is also invartiant under the global SU(2) transformation [itex]\phi \to e^{i \theta^{a} T_{a}}\phi[/itex]. So, “before and after the spontaneous symmetry breaking” the global symmetry group of [itex]\mathcal{L}[/itex] is always [itex]SU(2) \times U(1)[/itex].wormwoodsilver101 said: