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- Thread starter llynne
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Drakkith

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mfb

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This has nothing to do with positrons. Do you mean protons?neutron+ positron relationship

Yes, they "spontaneously arise". Quarks (the parts in neutrons and protons) can "emit" and "absorb" them. Note the quotation marks, as those gluons are virtual particles.

Mesons consist of a quark and an antiquark, bound by the strong interaction (so they have gluons inside). They are not gluons.

Depends on the phenomenon you want to describe.Both are virtual?

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Bill_K

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Please give us an example of a situation involving a gluon that is not virtual.Depends on the phenomenon you want to describe.

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mfb

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The gluon discovery was based on 3-jet events. Those gluons were still virtual, but not so far away from the properties of real particles as far as I know.

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Particles which carry the quantum number "colour" interact with each other by exchanging gluons ("strong force"). Proton and neutron however are neutral with respect to the colour quantum number. As already mentioned in other replys, the quarks do have colour - they are glued to each other by gluons.

The interaction which binds neutrons and protons to nuclei, is called "nuclear force". This is a residual of the strong force but electromagnetic and weak force contribute to the nuclear force, too.

Phenomenolgically, the nuclear force is often described by the exchange of mesons between the nucleons. However, in principle, the standard model of particles is the theoretical base for describing nuclear forces. However, calculations are a challenge.

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ChrisVer

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With no offence- not knowing whether mesons are gluons or not, I doubt you'd know what virtual particles are all about. So an introductory book on elementary particles (eg Griffith's) would be recommended if you are interested in this field.

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ChrisVer

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What different interpretation do you have in mind?

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Drakkith

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In quantum field theories, particles are interpreted as excitations of a field.

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Nugatory

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An alternative to the standard model would have to do two things before it would be taken seriously. First, it would have to agree with the experiments that have already been done, at least as well as does the standard model. Second, it would have to predict something that the standard model doesn't, so that we can perform an experiment to see which one works better.

So far no one has found any such alternative.

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With no offence- not knowing whether mesons are gluons or not, I doubt you'd know what virtual particles are all about. So an introductory book on elementary particles (eg Griffith's) would be recommended if you are interested in this field.

Getting curious: what exactly do you think is wrong in my post?

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What different interpretation do you have in mind?

For instance effective field theories like chiral pertubation theory could be a candidate:

http://en.wikipedia.org/wiki/Chiral_perturbation_theory

These are promising attempts to describe the low energy region of strong interactions, where QCD perturbation theory is not applicable. BTW, this theory justifies the historical attempt to describe nuclear forces by the exchange of mesons:

Wiki said:The theory allows the description of interactions between pions, and between pions and nucleons (or other matter fields). SU(3) ChPT can also describe interactions of kaons and eta mesons, while similar theories can be used to describe the vector mesons. Since chiral perturbation theory assumes chiral symmetry, and therefore massless quarks, it cannot be used to model interactions of the heavier quarks.

Although not being a fundamental renormalizable quantum field theory, these effective theories are used a lot by theoreticians.

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Drakkith

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Getting curious: what exactly do you think is wrong in my post?

I don't think he was referring to you in that post.

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ChrisVer

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i was referring to OP

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ChrisVer

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As I said, it was a recommendation rather than an offence (I didn't call you stupid or anything- i don't believe in such a thing in the first place). Just a way for both sides to understand what each other is speaking about.

In the mathematical procedure, gluons appear because strong interactions can be described as a local SU(3) gauge theory.

So let's start from the analogy of the electromagnetic field. The electromagnetic field comes when you impose local U(1) gauge invariance. In general a U(1) transformation will be:

[itex] Φ\leftharpoondown e^{iYa(x)}Φ [/itex]

If you put the transformed expression into the lagrangian, you will see that it's not invariant as it is... The kinetic term:

[itex] L=∂_{μ}Φ ∂^{μ}Φ^{*}[/itex]

will give you an extra term containing the partical derivative of [itex]a(x)[/itex] since it's a local transformation and thus depends on spacetime [itex]x[/itex] (i denote [itex]x^{μ}[/itex] as just [itex]x[/itex] here). Nevermind, to avoid the whole maths, you will have to introduce a new field to keep the invariance, which in fact will change your partial derivative to covariant derivative... Furthermore new interactive terms will be allowed for your local U(1) transformation invariance (the term will correspond to the "electromagnetic" field).

If you do the same for SU(3) (by keeping in mind it's not an abelian group) you will get also another field that will correspond to its interaction with itself. That'll be the field of gluons.

Again it's a model (QCD) that works nicely in explaining what we see, and that's why we have it. For example it was at the first stages of studying nuclear forces that physicists put in action the String Theory. Of course (since it's a fact now) QCD dropped it out.

The problem is that at low energies, the coupling constant of QCD is not working perturbatively because it is too big to give any reasonable result (higher orders will be more important and stuff). In that region, someone uses effective theories like mesons. The energies of nuclei (~MeV) are in that region, so it would make no sense to use gluons as medians of interaction and uses the pion mesons interchanging models. At the energies of a proton (~1GeV) or more, QCD is a good perturbative theory (it works).

In the mathematical procedure, gluons appear because strong interactions can be described as a local SU(3) gauge theory.

So let's start from the analogy of the electromagnetic field. The electromagnetic field comes when you impose local U(1) gauge invariance. In general a U(1) transformation will be:

[itex] Φ\leftharpoondown e^{iYa(x)}Φ [/itex]

If you put the transformed expression into the lagrangian, you will see that it's not invariant as it is... The kinetic term:

[itex] L=∂_{μ}Φ ∂^{μ}Φ^{*}[/itex]

will give you an extra term containing the partical derivative of [itex]a(x)[/itex] since it's a local transformation and thus depends on spacetime [itex]x[/itex] (i denote [itex]x^{μ}[/itex] as just [itex]x[/itex] here). Nevermind, to avoid the whole maths, you will have to introduce a new field to keep the invariance, which in fact will change your partial derivative to covariant derivative... Furthermore new interactive terms will be allowed for your local U(1) transformation invariance (the term will correspond to the "electromagnetic" field).

If you do the same for SU(3) (by keeping in mind it's not an abelian group) you will get also another field that will correspond to its interaction with itself. That'll be the field of gluons.

Again it's a model (QCD) that works nicely in explaining what we see, and that's why we have it. For example it was at the first stages of studying nuclear forces that physicists put in action the String Theory. Of course (since it's a fact now) QCD dropped it out.

The problem is that at low energies, the coupling constant of QCD is not working perturbatively because it is too big to give any reasonable result (higher orders will be more important and stuff). In that region, someone uses effective theories like mesons. The energies of nuclei (~MeV) are in that region, so it would make no sense to use gluons as medians of interaction and uses the pion mesons interchanging models. At the energies of a proton (~1GeV) or more, QCD is a good perturbative theory (it works).

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Drakkith

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Have you looking into what quantum field theories are?

Here's a link if you haven't.

http://en.wikipedia.org/wiki/Quantum_field_theory

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ChrisVer

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Bogoliubov & Shirkov- introduction to the theory of quantized fields (1959)

Bjorken & Drell- relativistic quantum mechanics (1964)

Cheng & Li- Gauge theories of elementary particle physics (1984)

Peskin & Schroeder- An introduction to Quantum field theory (1995)

Weinberg- The quantum theory of fields (1995)

Ryder- Quantum field theory (1996)

From them, you can have your own look and choose which fits in your needs and stuff... :)

Bjorken and Drell are just a good introduction to let you think and I don't think they formulate the QFT in the normal formalism (with the Lagrangians and stuff), but it's still nice and helped me a lot.

Also I was personally helped by Schroeder and Peskin and by Cheng and Li...

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Thanks very much, that's a very helpful list..

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