Hello, I am currently studying spontaneous symmetry breaking in qft. Several textbooks I've read prove Goldstone's theorem under supposing that(adsbygoogle = window.adsbygoogle || []).push({});

1) There exists a continuous global symmetry under which the Lagrangian is invariant.

2) The vacuum state is not annihilated by the conserved charge(or, alternatively, a field has a non-zero vacuum expectation).

Later it is said that theories with a gauge symmetry do not satisfy these hypothesis and so the goldstone theorem is invalid. In fact, a massive boson appears and not a massless one.

My question is how does a gauge symmetry violate the two hypothesis. Since it is a local symmetry, it also contains the global symmetry(the transformation is independent of spacetime) and so it should have the same conserved currents and charges.

I am guessing this is why Higgs won the nobel prize xD

Thank you

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# Why is goldstone's theorem incorrect in gauge theories?

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