The claymath 4-d QFT problem and virtual particles (as an example)

[billtodd]

I am trying to understand how would one opt to solve this open problem?, if there are some objects in the non-constructive-axiomatic QFT which mathematically are ill-defined.
One such ill defined notion is of virtual particles.

I tried to understand what constitutes a virtual particle. For example we have photons that are real which don't have mass as opposed virtual photons that do have mass. And then there are gluons which appear to be all of them virtual, and none are "real"; What does that mean?
Ok, I think I understand it now; It seems according to Wiki, that a virtual particle has mass that it's off-shell vs a real particle which its mass is on-shell, i.e. one satisfies the following relation: $E^2=(pc)^2-(mc^2)^2$ which is on shell and the other doesn't satisfy this.

Well I was under the impression that on-shell satsifies: $m^2=-k^2$ and off-shell doesn't, or vice versa.

Anyway, why can't a gluon also have a real partner, I read in Google that gluons only come as virtual particles and they have zero mass; But then are they on-shell or off-shell?

 

[weirdoguy]

Try this insights:
https://www.physicsforums.com/insights/misconceptions-virtual-particles/
https://www.physicsforums.com/insights/what-are-virtual-particles-intro/
https://www.physicsforums.com/insights/physics-virtual-particles/

 

[PeterDonis]

I read in Google

Where? Please give a specific reference.

 

[billtodd]

Where? Please give a specific reference.

Try searching in Google:"are gluons virtual or real?"
https://www.quora.com/Are-gluons-on...ticles like,virtual while gluons only virtual.

 

[PeterDonis]

Try searching in Google:"are gluons virtual or real?"

That's not an acceptable reference. First, a Google search is not a specific reference. Second, a Google search will turn up all kinds of nonsense.

https://www.quora.com/Are-gluons-only-virtual-particles-or-real-particles#:~:text=Gluons are massless particles like,virtual while gluons only virtual.

If this is the article you are actually referencing, it's a questionable reference, and it references Wikipedia, whose reliability is also questionable (some Wikipedia articles are quite reliable, but it's hard to tell which ones unless you already know the subject matter). You really need to be looking at a textbook or peer-reviewed paper.

But in any case, note that the Quora answer does not say "gluons" period are always virtual, it says "gluons in protons", which is not the only place gluons can be found.

 

[PeterDonis]

Moderator's note: Thread level changed to "I".

 

[billtodd]

That's not an acceptable reference. First, a Google search is not a specific reference. Second, a Google search will turn up all kinds of nonsense.


If this is the article you are actually referencing, it's a questionable reference, and it references Wikipedia, whose reliability is also questionable (some Wikipedia articles are quite reliable, but it's hard to tell which ones unless you already know the subject matter). You really need to be looking at a textbook or peer-reviewed paper.

But in any case, note that the Quora answer does not say "gluons" period, it says "gluons in protons", which is not the only place gluons can be found.

Which other places can gluons be in?
And are there gluons which are real i.e. on-shell?

 

[PeterDonis]

are they on-shell or off-shell?

"On shell" and "off shell" only make sense in the context of perturbation theory, but the strong interaction cannot be properly treated using perturbation theory, at least not in any context relevant for addressing the questions you are asking about gluons. So this question is unanswerable because it's not well posed.

 

[billtodd]

"On shell" and "off shell" only make sense in the context of perturbation theory, but the strong interaction cannot be properly treated using perturbation theory, at least not in any context relevant for addressing the questions you are asking about gluons. So this question is unanswerable because it's not well posed.

So how do you define a virtual vs real particle in non-perturbative QCD?
This begins to be interesting.
I read in the Wiki page that of virtual particles, that in Lattice Gauge Theory there's no use of this distinction between virtual and real.

P.S
Believe me if I'll stay alive long enough I'll read the other books on non-perturbative QCD, but I first need to finish the red book on perturbative QCD.

 

[PeterDonis]

how do you define a virtual vs real particle in non-perturbative QCD?

You don't. The concept of virtual vs. real particle only makes sense in perturbation theory.

 

[billtodd]

You don't. The concept of virtual vs. real particle only makes sense in perturbation theory.

It's interesting, and I thought that split-personality of physics appears only in the problem of quantum gravity in high energies, while you say that there this dichotomy between perturbation theory and non-perturbation and they don't coincide at least in this regard of virtual vs real.
I found an interesting and quite dated debate here in PF:
https://www.physicsforums.com/threads/non-perturbative-qft-without-virtual-particles.485597/

 

[PeterDonis]

there this dichotomy between perturbation theory and non-perturbation and they don't coincide at least in this regard of virtual vs real

This "dichotomy" is purely in our theoretical models. There is no such dichotomy in reality. The gluons don't know that they're not supposed to be doing "perturbation theory".

 

[billtodd]

This "dichotomy" is purely in our theoretical models. There is no such dichotomy in reality. The gluons don't know that they're not supposed to be doing "perturbation theory".

I wonder how to reconcile this mathematically.
Someone said that practically we may never know if PT is just a computational aid for computation, and there might be no need for such "virtual" vs "real" terminology, but then again someone can say that PT appears also in QM; and I don't think anyone thinks of dispensing with PT over there.
Are we bound to use PT in general (in both applied maths and theoretical physics) because of computer's limitations? i.e. there's no real rigorous mathematical justification of using PT in our problems?

I must confess that part of me of trying to write a thesis on PT in ODE or PDE is that I thought there's a rigorous justification for this theory; though my adviser warned me that there might not be such justification.
Otherwise I think I would have tried doing something on mathematical logic or something else in mathematical analysis.

 

[PeterDonis]

I wonder how to reconcile this mathematically.

Reconcile what?

Someone said

Who? You need to give specific references.

there's no real rigorous mathematical justification of using PT in our problems?

Physicists generally use tools that work, in the sense of making predictions that are accurate enough for their purpose, without worrying very much about whether there is a "rigorous mathematical justification". For example, they will happily compute the first few terms of a perturbation theory infinite series without worrying about whether the series converges, as long as the computation gives a result that matches experiment closely enough.

 

[jbergman]

I wonder how to reconcile this mathematically.
Someone said that practically we may never know if PT is just a computational aid for computation, and there might be no need for such "virtual" vs "real" terminology, but then again someone can say that PT appears also in QM; and I don't think anyone thinks of dispensing with PT over there.
Are we bound to use PT in general (in both applied maths and theoretical physics) because of computer's limitations? i.e. there's no real rigorous mathematical justification of using PT in our problems?

I must confess that part of me of trying to write a thesis on PT in ODE or PDE is that I thought there's a rigorous justification for this theory; though my adviser warned me that there might not be such justification.
Otherwise I think I would have tried doing something on mathematical logic or something else in mathematical analysis.

I believe that PT theory has been put on a rigorous footing. See this paper for more discussion. I'm talking out of my depth, here but I believe the problem with PT approaches are they only work if you treat QFT as an effective theory with energy cutoffs.

I believe the desire of the Yang Mills Clay problem is to construct a full non-effective QFT. Take what I've said with a large grain of salt.

 

[Adrian59]

I am trying to understand how would one opt to solve this open problem?, if there are some objects in the non-constructive-axiomatic QFT which mathematically are ill-defined.
One such ill defined notion is of virtual particles.

I tried to understand what constitutes a virtual particle. For example we have photons that are real which don't have mass as opposed virtual photons that do have mass. And then there are gluons which appear to be all of them virtual, and none are "real"; What does that mean?

My understanding is that a virtual particle is never detected on its own, as it is involved with the transmission of a force, so it is absorbed by the destination particle. As it is not detected it is deemed virtual. Of course the force carriers for the electromagnetic and weak forces have been detected independently but not the colour (UK spelling) force.
The issue of mass is not required for the argument as the mass given to a virtual photon is a fictitious mass which is only to prevent the integral having a divergence, and then this fictitious mass can be removed in the full renormalization calculation. Since the virtual photon is never detected itself, this infinitesimal mass is of no observational significance. I other words the fictitious mass is only a mathematical device.

 

[A. Neumaier]

So how do you define a virtual vs real particle in non-perturbative QCD?

In non-perturbative QCD, only real particles exist (gluons, mesons, baryons, and perhaps more complex bound states). Virtual particles are an artifact of perturbation theory.