
#37
Dec210, 06:58 PM

P: 2,281

I can describe the magnetic force in terms of the exchange of <insert noun>... and the EM force is real, but that doesn't mean that my description is an accurate one. It's just unfortunate that the name "virtual particle" ever came along... without it these discussions wouldn't exist. 



#38
Dec310, 12:24 AM

Sci Advisor
P: 5,307

I repeat my statement: 



#39
Dec310, 12:40 AM

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PF Gold
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#40
Dec310, 01:13 AM

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#41
Dec310, 03:38 AM

P: 200

Still, all virtual particles or virtual transitions I know are equally well described by a more technical term  'perturbative corrections'. Can you give me any example that a virtual particle arises in a nonperturbative context? 



#42
Dec310, 05:05 AM

P: 661

It's rather like asking if a photon "really" goes off to alpha centuri and whizzes around it a couple of times when doing a double slit experiment, since we have a mathematical formalism which considers such behaviour (path integral) and predicts correct results for the interference pattern observed. The intermediary mathematical constructs in QFT should surely not be considered "real" in any sense, in fact nothing should be considered "real" unless it can be observed, which essentially restricts "reality" to stable macroscopic constructs, since everything at the microscopic level is in probabilistic flux. 



#43
Dec310, 06:46 AM

P: 661

To clarify, by "microscopic" I mean ~planck scale.
And I realise Wilczek is suggesting that virtual particles are "real" by his definition. It's possible that with a "correct" simulation of reality at the scale of electrons and protons we may really see these virtual particles shooting around between particles, so it's possible Wilczek is right to think they are "real". On the other hand there may be a better way to mathematically model the microscopic, and with another model we may have no such particle exchanges. My feeling is that we will see something that can partially support the case for "reality" of the particles. 



#44
Dec310, 08:02 AM

P: 196

I could not resist to send the same question to Curtis Callan.
His answer 



#45
Dec310, 09:13 AM

Sci Advisor
P: 5,307

I repeat my question: Have you studied the paper I proposed?




#46
Dec310, 09:21 AM

P: 196





#47
Dec310, 10:04 AM

P: 661

At least Wilczek clearly demarcates between mathematical concept and reality. 



#48
Dec310, 10:52 AM

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P: 5,307

In this paper a "quantum gauge fixed" Hamiltonian is constructed for QED, which contains a static Coulomb term.
The gauge fixing is implemented via unitary transformations. There is a simple example in 1dim. QM, a twoparticle system with interaction V(xy). Instead of going to the c.o.m system, setting the total momentum P=0 and quantizing in x,p one first quantizes in x,y, ... and implementes P~0 as a constraint. The space of physical states is then described by the states p, P=0>, but X and P are still qm operators. In QED the constraint P~0 is replaced by the Gauss law constraint G~0. By a (complicated) unitary transformation the space of physical states is described via transversal photons, G=0>. The resulting Hamiltonian consists of  a kinetic photon term  a kinetic fermion term  an interaction term where fermions couple to dynamical photons to (*)  an interaction term where fermions couple to a static Coulomb potential (**) (*) would result in virtual particles in a perturbation expansion (**) is the wellknown Coulomb potential which looks like [tex]\hat{V}_C = e^2 \int d^3x\,d^3y\,\frac{\rho(x)\,\rho(y)}{xy}[/tex] The charge density in the numerator is just the 0^{th} component of the fourvector current density and looks like [tex]\rho = \bar{\psi}\gamma^0\psi[/tex] i.e. it is bilinear in the fermion fields. The conclusion is that virtual particles from (*) do not generate the Coulomb potential but only perturbations to the Coulomb potential. [This approach is heavily used in canonical, nonperturbative quantization of QCD. One applies unitary operators to define "dressed" fermion fields. Via this dressing the colorCoulomb potential (which contains gluon fields!) changes. The colorCoulomb potential is terribly complicated. One has to define a partial differential operator D[A] where A is the gluon field. In order to construct V one has to invert D which means that you have an Adependend integral operator with a kernel that has formally an Adependent denominator. You are not allowed to make a perturbation expansion as you would lose all information regarding the nonperturbative structure contained in 1/D which is responsible for color confinement.] Lessons learned: both the interaction potential and the definition of fermion fields are gauge dependent. Therefore the concept of virtual particles is gauge dependent, too. The Coulomb potential itself is not necessarily generated by oneparticle exchange but can (depending on the gauge) be described as a static term. 



#49
Dec310, 11:15 AM

P: 196

Thanks Tom for the very elaborated explanation, it's very much appreciated. Since you seem much more knowledgeable than me, I might need some time to understand what you just wrote here. One reason why I did not read the paper by myself was because it looked a bit over my head. I'm still learning QFT, you know!




#50
Dec310, 11:38 AM

PF Gold
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#51
Dec310, 12:25 PM

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#52
Dec310, 12:28 PM

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#53
Dec310, 06:27 PM

P: 196

Hey Tom, I stared at you post for several minutes and I think it makes sense, as far as I can judge. Even tough it is still not 100 percent clear to me how it works that two nonaccelerated charges can exchange forces with each other, I take it from you that can work.
I found a very good thread on PF about virtual particles. I like to quote two excellent posts. Especially I like the second post, which is somewhat reconciling. post 14 by Igor 



#54
Dec310, 06:35 PM

Sci Advisor
P: 5,307

It looks like an ordinary Coulomb term from Maxwell's theory. The main difference is that the charge densities are operators acting on a (fermionic sector of the QED) Hilbert space 


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