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I know that a global symmetry implies the presence of a conserved charge but how it does affect the particle spectrum? and in this sense what is the difference with a gauge symmetry?

Anna
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    I'm not sure what you mean by the symmetry "affecting" the particle spectrum. Would "the particles have to carry a representation of the symmetry group" be such an affect? – ACuriousMind Apr 12 '20 at 11:38

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  1. Gauge symmetry is not symmetry, it is redundancy in description of field in QFT. It remove unphysical degrees of freedom, that we need to have clearly Lorentz-invariant formulation. So gauge symmetry doesn't affect spectrum.

  2. Global symmetry may be spontaneously broken by vacuum expectation value or be unbroken. In second case all particles sit in representation of global group. In first case appear Goldstone bosons (# of g.b. = # broken generators), which signal about symmetry breaking.

Nikita
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  • "gauge symmetry doesn't affect spectrum" 2. "it rather remove unphysical states from spectrum" sounds like a contradiction to me, though I think I understand what you are trying to say. Maybe try wording it better?
    • – Prof. Legolasov Apr 12 '20 at 10:54
  • Also, gauge symmetries can be "broken", too (the Higgs mechanism). – Prof. Legolasov Apr 12 '20 at 10:59
  • I slightly edited answer. I think it's clear what I mean. Gauge symmetry is redundancy and can't be broken. You wrote "broken", so realize it. – Nikita Apr 12 '20 at 11:36
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    @Nikita your first point is still unclear and self-contradictory. – ɪdɪət strəʊlə Apr 12 '20 at 11:52
  • @st.vit , I once more edited answer. Maybe you can ask concrete question, to understand, how to improve answer? – Nikita Apr 12 '20 at 12:20
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    Nikita you have to be careful with terminology. This answer is correct in spirit, but it contains a contradiction in its formulation (as of now, and before). First you say that the gauge symmetry removes unphysical degrees of freedom from the spectrum. On the next like, you write "So gauge symmetry doesn't affect spectrum". I don't see the implication and in fact "removes degrees of freedom from the spectrum" clearly implies altering the spectrum, which is the exact opposite of your conclusion. – Prof. Legolasov Apr 12 '20 at 12:25
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    I think this confusion stems from that the question itself (relation of symmetry to spectrum) is ill-posed. Models enjoy symmetries and they have a spectrum associated to them, which doesn't mean that one follows from another or vice versa. Maybe you could go more into this and try to clear this confusion in your answer. – Prof. Legolasov Apr 12 '20 at 12:27
  • @Prof.Legolasov, now in post aren't anything about "removes unphysical degrees of freedom from the spectrum". I agree, there's no such states in spectrum from begin. – Nikita Apr 12 '20 at 12:50