## The main arguments for Higgs

I'll now illustrate how the Higgs particle makes mass with a toy model: electromagnetism with a complex charged scalar, a Higgs-like field.

Its Lagrangian:
$L = - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 ((\partial_\mu - iqA_\mu)\Phi)((\partial^\mu + iqA^\mu)\Phi^*) + \frac12 V(|\Phi|^2)$
Electromagnetic kinetic-energy, scalar kinetic-energy with electromagnetic interaction, scalar potential terms.

Let $\Phi = \phi e^{i\theta}$
where both quantities on the right are real. The Lagrangian becomes
$L = - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 \partial_\mu\phi \partial^\mu\phi + \frac12 (\partial_\mu\theta - qA_\mu)(\partial^\mu\theta - qA^\mu)\phi^2 + \frac12 V(\phi^2)$
The $\phi$ is a neutral scalar field, and the $\theta$ is the Goldstone mode. Do a gauge transformation on the electromagnetic field:
$A_\mu \to A_\mu + \frac{1}{q}\partial_\mu\theta$

The Lagrangian becomes
$L = - \frac14 F_{\mu\nu} F^{\mu\nu} + \frac12 \partial_\mu\phi \partial^\mu\phi + \frac12 (q\phi)^2 A_\mu A^\mu + \frac12 V(\phi^2)$
The third term has the form of a mass term, with a mass
$m = q\phi$

The Lagrangian has become a Lagrangian for a neutral scalar field and a massive photon, with the Goldstone mode disappearing into the latter.

I hope that I got that right.
 1. But the root of arising of masses is in quantum gravity (QG). It also defines natural units of mass, Planck's mass. So, how Higgs boson can be linked with QG? OK, it is known, supersymmetry, and additional dimensions. Can it go simpler, without this? 2. As visible in http://physicsworld.com/cws/article/...-but-what-sort there are some different probabilites for decay channels, as predicted. How this can influence on properties of Higgs, such as that it is a creator of masses? Ok, one argument is that Higgs boson was found where it was expected...
 I do not see, how Higgs mechanism is in agreement with GR. GR says that elementary particles build space-time. Thus, if all matter is removed from our universe, nothing remains, neither universe. But, in Higgs mechanism space-time help to interact among particles and Higgs boson. The only possible explanation, which I see, is that principles of GR are valid only in macroword?

 Quote by exponent137 I do not see, how Higgs mechanism is in agreement with GR. GR says that elementary particles build space-time. Thus, if all matter is removed from our universe, nothing remains, neither universe.
GR says nothing like that. Without particles the space-time would be flat (Minkowski) but it would still be there.

 Quote by exponent137 But, in Higgs mechanism space-time help to interact among particles and Higgs boson.
Nope. In Higgs mechanism Higgs field interacts with particles. Space-time acts the same as it does in all QFT - as background.

 Quote by exponent137 The only possible explanation, which I see, is that principles of GR are valid only in macroword?
This may very well be true.

 Quote by Dead Boss Nope. In Higgs mechanism Higgs field interacts with particles. Space-time acts the same as it does in all QFT - as background.
Yes, but in GR there is no background, there is contradiction. If GR is macro effect, how then background exists in microworld?

 Quote by Dead Boss GR says nothing like that. Without particles the space-time would be flat (Minkowski) but it would still be there.
I do not agree with this.
Sean Carroll: http://arxiv.org/pdf/gr-qc/9712019.pdf page 138:

Let’s put some of these ideas into the context of general relativity. You will often hear it proclaimed that GR is a “diffeomorphism invariant” theory. What this means is that, if the universe is represented by a manifold M with metric gμν and matter fields ψ, and φ : M → M is a diffeomorphism, then the sets (M, gμν , ψ) and (M, φ∗gμν, φ∗ψ) represent the same physical situation. Since diffeomorphisms are just active coordinate transformations, this is
a highbrow way of saying that the theory is coordinate invariant. Although such a statement is true, it is a source of great misunderstanding, for the simple fact that it conveys very little
information. Any semi-respectable theory of physics is coordinate invariant, including those based on special relativity or Newtonian mechanics; GR is not unique in this regard. When people say that GR is diffeomorphism invariant, more likely than not they have one of two
(closely related) concepts in mind: the theory is free of “prior geometry”, and there is no preferred coordinate system for spacetime. The first of these stems from the fact that the
metric is a dynamical variable, and along with it the connection and volume element and so forth. Nothing is given to us ahead of time, unlike in classical mechanics or SR. As a consequence, there is no way to simplify life by sticking to a specific coordinate system
adapted to some absolute elements of the geometry. This state of affairs forces us to be very careful; it is possible that two purportedly distinct configurations (of matter and metric) in GR are actually “the same”, related by a diffeomorphism. In a path integral approach
to quantum gravity, where we would like to sum over all possible configurations, special care must be taken not to overcount by allowing physically indistinguishable configurations to contribute more than once. In SR or Newtonian mechanics, meanwhile, the existence
of a preferred set of coordinates saves us from such ambiguities. The fact that GR has no preferred coordinate system is often garbled into the statement that it is coordinate invariant (or “generally covariant”); both things are true, but one has more content than the other.

Remark: Minkowski space is preferred coordinate system.

Mentor
 Quote by exponent137 1. But the root of arising of masses is in quantum gravity (QG). It also defines natural units of mass, Planck's mass. So, how Higgs boson can be linked with QG?
Whoever answers this question convincingly will be a strong candidate for a Nobel Prize.

 Quote by jtbell Whoever answers this question convincingly will be a strong candidate for a Nobel Prize.
Yes, but above I gave question, how Higgs mechanism cannot be in contradiction with general relativity.

 Quote by exponent137 I do not agree with this. Sean Carroll: http://arxiv.org/pdf/gr-qc/9712019.pdf page 138: Remark: Minkowski space is preferred coordinate system.
I agree that it was a bit too strong statement. What I meant is that space-time is meaningful concept on it's own. Vacuum solutions to EFEs are relevant and perfectly physical.
 When Higgs boson will be completely proved, thus this means that this will be the main proof that elementary particles are not black holes or that gravity does not make elementary particles? What are EFEs? If space-time is meaningful concept on it's own, this is against GR.

 Quote by exponent137 What are EFEs?
Einstein's field equations.

Mentor
 Quote by exponent137 When Higgs boson will be completely proved, thus this means that this will be the main proof that elementary particles are not black holes or that gravity does not make elementary particles?
No, as the Standard Model does not include gravity anyway. On the other hand, most concepts to unify gravity and the other interactions have supersymmetry as a feature, and this has multiple Higgs particles. If there is just one, it might become tricky for some SUSY models, at least for the minimal supersymmetric model (MSSM).

 Quote by mfb No, as the Standard Model does not include gravity anyway. On the other hand, most concepts to unify gravity and the other interactions have supersymmetry as a feature, and this has multiple Higgs particles. If there is just one, it might become tricky for some SUSY models, at least for the minimal supersymmetric model (MSSM).
I ask because if Higgs mechanism creates masses of particles, gravitational self-interaction cannot make them? One or the other.
 An electron in a semi-conductor has changed mass. Is there any similarity between mass given by Higgs boson and this "semi-conductor" mechanism? I forget also, what is the principle of electron mass change in semi-conductor?
 Now I found derivation of effective electron mass in semi conductor http://en.wikipedia.org/wiki/Effecti...state_physics) It is in the section "derivation". Is any similar principle for Higgs boson?

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