Monday 23 October 2017

spacetime - When it is said that the Higgs field is a scalar, do they mean Lorentz scalar?


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?



Answer



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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