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LedPhoton
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Hello, I am currently studying spontaneous symmetry breaking in qft. Several textbooks I've read prove Goldstone's theorem under supposing that
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
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