Graduate Higgs particle and non-zero expected value in vacuum

[Adams2020]

TL;DR

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

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

 

[mfb]

The vacuum expectation value is a property of the Higgs field, not the Higgs boson. There are no Higgs bosons in the vacuum.

A vacuum expectation value for a non-scalar field would imply some preferred direction and reference frame: It would change if you go to a different reference frame, i.e. break Lorentz invariance.

 

[ChrisVer]

It is a weirdly put phrase, written by someone who probably already knew of the existence of the Higgs field (?)
I've seen tensor fields having non-vanishing vevs (but of course we don't have any in the SM). This however makes me say that, in principle, there is nothing extremely special about scalars. One special thing they have is that they have nice and easy Lorentz Transformations and that we know of the Higgs boson.
I know that vector fields have problems as they indeed give a preferred direction to the vacuum if you give them non-vanishing vev.

 

[samalkhaiat]

It is a weirdly put phrase, written by someone who probably already knew of the existence of the Higgs field (?)
I've seen tensor fields having non-vanishing vevs (but of course we don't have any in the SM). This however makes me say that, in principle, there is nothing extremely special about scalars.

No, the statement is correct and can be proven mathematically. To keep the Poincare symmetry intact, only scalar fields can develop non-zero VEVs.