We often hear that Higgs boson is a scalar boson, and that Higgs field is a scalar field. I was always thinking that this means "4-scalar". In other words, it is space-time invariant, .i.e. it's properties are not changing if move relative to it. Unlike photon which changes it's frequency, polarization and other properties, if we look at it from moving frame, Higgs is always the same.

Is above correct? If not then what is correct and what is not?

  • $\begingroup$ Where did you read 4-scalar. And note that polarization (helicity, in this case, also chirality) does not change for massless particles (photons). $\endgroup$
    – jinawee
    Dec 11, 2013 at 14:43

1 Answer 1


You are right, in this case, scalar means Lorentz invariant field. But it is not invariant under the transformations of SU(2)xU(1) of the electroweak model. And it is a scalar under the SU(3) of QCD.

So the four real components of the Higgs are indeed invariant under space-time transformations.

Physicists are usually not very clear in these distinctions, and you have to guess under which transformation the field is a scalar.

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    $\begingroup$ It has spin 0, no? The spin is what usually physicists focus on when talking of scalars. $\endgroup$
    – anna v
    Dec 11, 2013 at 16:04
  • $\begingroup$ @annav: Yes, the spin is zero. But that's exactly the problem of the OP : physicists usually talk of scalar with respect to the Lorentz transformations (which include rotations and thus spins), but the term scalar just mean in principle "belonging to the trivial representation of a given group", and this group can be the Poincarre group, U(1), SU(N), O(N), etc. And fields can be scalar of one group and not the others, but you usually have to guess depending on the context. $\endgroup$
    – Adam
    Dec 11, 2013 at 16:09
  • $\begingroup$ As scalar as the electron mass? $\endgroup$ Dec 11, 2013 at 17:35
  • $\begingroup$ I agree, though in BSM models, especially SUSY, one talks of pseudoscalar Higgs. In this case, one is referring to CP. $\endgroup$
    – innisfree
    Dec 11, 2013 at 17:36
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    $\begingroup$ @SuzanCioc: The Higgs field is in fact a two-dimensional complex vector of the electroweak symmetry SU(2)xU(1) (therefore it has four real components). Each component is a scalar field with respect to the Poincarre group. Scalar or vector depend on what transformation/symmetry we're talking about. See also wiki en.wikipedia.org/wiki/… $\endgroup$
    – Adam
    Dec 11, 2013 at 19:54

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