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What does the phrase “Due to Lorentz invariance, only the Higgs particle can have a non-zero expected value in a vacuum” mean?

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    $\begingroup$ We need some context here. Any scalar field can have a vacuum expectation value. So what does "only" mean? Was there a list? $\endgroup$ – mike stone Oct 13 at 15:58
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    $\begingroup$ @mikestone I assume OP refers to the fact that the Higgs field is the only scalar field in the standard model, so if we accept that only scalars can have a nonzero VEV then the Higgs is the only SM field that can have nonzero VEV. $\endgroup$ – Bence Racskó Oct 13 at 16:01
  • $\begingroup$ I agree, see e.g. this: physics.stackexchange.com/a/108114/226902 $\endgroup$ – Quillo Oct 13 at 16:45
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It is the Higgs field, not the Higgs particle, that has a nonzero vacuum expectation value (VEV).

The Higgs field is a scalar field. Scalar fields don’t have a direction in spacetime; they just have a value. Other fields such as spinor fields (for electrons, quarks, and neutrinos) and vector fields (for photons, gluons, and weak bosons) do have a direction in spacetime. (In the case of spinors, I’m simplifying a bit.) Lorentz transformations change this direction, so a VEV for spinor and vector fields could not be Lorentz-invariant; for the scalar Higgs it can.

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  • $\begingroup$ Nince answer. Can you please tell me where the graviton would fall into, which group? Vector field and thus that one can't have nonzero VEV either? $\endgroup$ – Árpád Szendrei Oct 14 at 5:41
  • $\begingroup$ Gravitons are represented by a tensor field with two indices. As with a vector field with one index, a nonzero VEV for such a field would not be Lorentz-invariant. $\endgroup$ – G. Smith Oct 14 at 5:47

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