Higgs field

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  • #26
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I have a question about this topic. If quarks were massless (gedanken experiment), then wouldn't pions be massless (goldstone bosons) ?
yes of course, everybody agrees that pions would be exact Goldstone bosons in that case. In fact, we would have tons of problems if the quarks were exactly masselss, already in QED BTW.
Thas would mean in that case we would have a composite massless particle which is not so common in our present knowledge of the world ?
I gave up making a list of all the conceptual problems that would lead to.
 
  • #27
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I guess what I'm wondering is do constituent mass and the mass imparted by the Higg's Field follow the same exact law of gravity?

And as an addendum, I was wondering if it's known where inertia fits; (i.e. if there's a separate particle proposed to be responsible for inertia, or if inertia is some consequence of conventional gravity)
You may want to review classical mechanics in the lagrangian formulation. Classical mechanics is the limit of quantum mechanics when the action involved is large compared to Planck's constant. Quantum mechanics follows from the non-relativistic limit of quantum field theory. This is a bit sketchy but should indicate you that we do have inertia in the standard model.

The fact that inertial mass and gravitational mass are the same is one of the basic assumptions of general relativity and can be considered valid as we have no experimental hint that it might not hold. Gravitation however is not addressed in the standard model.

Doksh_itzer has dubbed quarks INFOs, for (well) identified non-flying objects. They are probably far more interesting than UFOs, but being confined the question of their mass is quite a tricky one. There are entire books devoted to this issue. The "constituent mass" interpretation lies far remotely from gravitational problems. It is an effective mass, the kind of arising for instance to describe electrons moving in a ion lattice : their propagation undergoes constant random scattering resulting in an apparent mass larger than the free mass. As you can guess, there is a rigourous formalism behind, giving this effective mass the interpretation of an (effective) inertial mass. I am not quite sure what to comment about the corresponding (effective ?) gravitational mass however. It seems at first glance to me that those kinds of gravitational and effective mass should also be the same, because what really happens is that you want to replace a light mass with a fluctuating high momentum by a larger mass and a lower (more or less) constant momentum. Needs more thoughts though...
 
  • #28
kdv
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You may want to review classical mechanics in the lagrangian formulation. Classical mechanics is the limit of quantum mechanics when the action involved is large compared to Planck's constant. Quantum mechanics follows from the non-relativistic limit of quantum field theory. .....

Do you have a reference for that? where sonmeone starts from QFT and shows clearly how one recovers quantum mechanics by taking a well defined non-relativistic limit? I know that this is what one expects but I have never seen it done explicitly.
 
  • #29
Pythagorean
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Thank you for a well-rounded answer. I remember a bit of the Lagrangian stuff we did for generalized coordinates. Very impressive technique.

It is an effective mass, the kind of arising for instance to describe electrons moving in a ion lattice : their propagation undergoes constant random scattering resulting in an apparent mass larger than the free mass.

I took Solid State, and I remember this arising. This sort of implied to me that the actual mass of the object wasn't changing, and that it was a convenient math trick.

I must admit though, that a lot of Solid State went over my head. I took it before I took quantum or thermo, and Kittel didn't seem to match the lectures that great. Some of the homework problems didn't seem to have any development in the text either, so I could be far off in my perspective of effective mass in electrons/phonon interactions (that it is a mathematical trick and not physically true).
 
  • #30
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Do you have a reference for that? where sonmeone starts from QFT and shows clearly how one recovers quantum mechanics by taking a well defined non-relativistic limit? I know that this is what one expects but I have never seen it done explicitly.
These kind of things are usually not done in introductory textbooks, since they are more relevant to research programs really. Full blown calculation wavefunctions are kind of hairy, but tractable as you can guess from Baez's stuff on virtual particles.

However, you can find many references, even on this forum ! (see [thread=124893]this thread[/thread] for instance, with plenty of excellent references, especially from nrqed who has not been around for a few months apparently).

In addition, I'm sure condensed matter people would have more references.
 

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