We need a "magnetic" Higgs field? The Higgs boson spin is 1?

UPDATE July 6, 2022: A scalar field can be Lorentz covariant. See our note in the next blog entry.

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In the update to the previous blog post we noted that if a fast moving observer in his frame displaces a volume S of the Higgs field to a value z, then a static observer will see the volume smaller, and see the energy in  the displacement smaller than the fast moving observer. This contradicts special relativity.

Can a scalar field be Lorentz covariant?

Let us try to form a scalar field theory from the electric Coulomb potential. That is, we assume that the magnetic vector potential is zero.

One runs into difficulties in making the scalar field theory Lorentz covariant. This suggests that a scalar field theory cannot be Lorentz covariant. One must introduce a magnetic form of the field to obtain Lorentz covariance.

If a field has an electric and a magnetic component, then it has an associated 4-vector and the spin of the quantum should be 1.

https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HIGG-2013-01/

The LHC measured that the spin of the Higgs particle is 0. How do we explain this discrepancy? Could the very short lifetime of the particle explain this?

If the spin of the Higgs particle is 1, then its angular momentum may have values +1, 0, -1. Could it be that the LHC experiment for some reason only produces the 0 variety?

In quantum mechanics, scalar field theories are used as toy models in teaching. They are probably ok if we study nonrelativistic phenomena.

Symmetry breaking would break the Galilei symmetry and Lorentz covariance

We think that symmetry breaking is something which is not Lorentz covariant. If we have a crystal, then its lattice defines preferred directions in space, which contradicts the Galilei symmetry.

In a previous blog post we explained that, in a sense, symmetry is not broken in the Higgs model. Thus, the Higgs model does not have this problem.

Conclusions

The Higgs field in the Standard Model is strange: it is the only scalar field and its quantum has the spin 0. Ockham's razor suggests that we should not introduce a field which differs from all the other fields that we know.

If a scalar field cannot be Lorentz covariant, then we must introduce a magnetic Higgs field. The spin of the quantum should then be 1.

Does a magnetic Higgs field spoil its function as the generator of mass?

Can we add a magnetic Higgs field? The "velocity" of the Higgs field is not defined. How do we define the magnetic Higgs field?