What is the Higgs boson's mechanism for giving mass?
Don Lincoln, a FermiLab scientist and educator, answers your question here:
OK, so the Higgs boson interacts with particles to give them mass (as per the previous movie) but still, does anyone know the mechanism of interaction?
Yes, it is called "the Higgs mechanism".
For an intro see http://en.wikipedia.org/wiki/Higgs_mechanism
and the references.
does anyone here know what the Higgs mechanism is?
Did you read the wikipedia page? Since you replied a minute after it was posted, I gather that you did not. If you did, what is there on that page that you do not understand?
To clarify: it's the interaction with the Higgs field that gives gauge particles mass. The Higgs boson is the excitation of this field.
quite a bit actually. The wiki post and my post were only a coincidence. The math of the wiki post notwithstanding, it is really that simple?
"Don't shoot, it's only me," Bob hope 1990.
"Simple"? It is simple if you make the model so simple that it is a very rough, and often misleading description of the actual physics.
is the Higgs field equivalent to space itself?
No. It's just like any other quantum field, except that there is a property of the Higgs field that is nonzero in space.
do the particles that are given mass by the Higgs field affect the Higgs field?
Yes. For example, the mass of the Higgs particle depends on all the particles to which the Higgs couples. More generally, any property of the Higgs that gets renormalized depends on all such particles.
In general is the technique of renormalization required because of interactions?
I know the question is vague. That's because there's a lot i don't know.
Actually the Higgs field in the vacuum should be so strong that according to Nobel laureate Veltman the universe would collapse to the size of a football.
That's the energy of the Higgs vacuum; I'm referring to the vacuum expectation value of the field. The latter is definitively nonzero, the former is unknown. I have no idea Veltman thinks there needs to be an energy associated with the Higgs field that would cause the universe to collapse.
Can you explain the difference?
On slide 17 of http://www.nikhef.nl/pub/theory/academiclectures/Higgs.pdf Veltman explains how he reaches this conclusion.
That is correct.
See the figure in this post: http://dorigo.wordpress.com/2007/11/10/the-goldstone-theorem-for-real-dummies/. The values +/- [itex]\nu[/itex] are the vacuum expectation values of the field for the corresponding vacuum. The Higgs starts in the middle, at the local maximum (the false vacuum), and rolls down to one of the minima (true vacua). The energy of the true vacua, [itex]V(\pm \nu)[/itex], is the vacuum energy of the Higgs. So the vacuum expectation value of the field and the vacuum energy are different things. It is generally assumed that [itex]V(\nu)=0[/itex], but this is really just put in by hand. If [itex]V(\nu)<0[/itex], then the universe should collapse if the Higgs field is dominating the energy density of the universe (this might be what Veltmann is talking about). Otherwise, if [itex]V(\nu)>0[/itex], the universe should inflate once the Higgs field dominates.
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