Insights Misconceptions about Virtual Particles - Comments

[vanhees71]

Well, in my QFT lecture nobody taught "vacuum fluctuations", nor do I in my lectures ;-). There are radiative corrections, symbolized by Feynman diagrams containing loops, and these Feynman diagrams are just a very clever method to write down complicated formulae in a very efficient way. The "real" thing, i.e., what's measurable calculated in this way are transition-probability matrix elements $|S_{fi}|^2$, which usually are expressed in terms of cross sections and which are measured by the experimentalists with there detectors. There's not a single observation of "vacuum fluctuations", and there never can be, because to measure something you have to use a detector, and introducing a detector makes the situation not to be vacuum anymore.

The Casimir effect is indeed, as discussed at length in this thread and elsewhere here on the forums, indeed pretty analogous to the van der Waals force. It's not due to fluctuations of the vacuum but due to quantum fluctuations of real (not virtual!) charges and fields.

 

[Karolus]

Nothing is a hoax. It is a different way to describe things. You can use virtual particles - just keep in mind that they are mainly a mathematical tool in perturbation theory. Their existence is about as real as the existence of an integral sign, another mathematical tool used in perturbation theory.

So even an electron is as real as the psi schrodinger, as real as a Greek letter or mass is just as real a Latin letter ...
in short, all of physics is as real as a series of mathematical signs...

 

[Karolus]

Well, in my QFT lecture nobody taught "vacuum fluctuations", nor do I in my lectures ;-). There are radiative corrections, symbolized by Feynman diagrams containing loops, and these Feynman diagrams are just a very clever method to write down complicated formulae in a very efficient way. The "real" thing, i.e., what's measurable calculated in this way are transition-probability matrix elements $|S_{fi}|^2$, which usually are expressed in terms of cross sections and which are measured by the experimentalists with there detectors. There's not a single observation of "vacuum fluctuations", and there never can be, because to measure something you have to use a detector, and introducing a detector makes the situation not to be vacuum anymore.

The Casimir effect is indeed, as discussed at length in this thread and elsewhere here on the forums, indeed pretty analogous to the van der Waals force. It's not due to fluctuations of the vacuum but due to quantum fluctuations of real (not virtual!) charges and fields.

So Feynman lost a lot of time to identify arrows as fermions, wavy lines as photons and so on .. a picturesque symbolism just to make a tattoo ... who knows, maybe his car, though as I read, had drawn them on his car ...

 

[mfb]

So even an electron is as real as the psi schrodinger, as real as a Greek letter or mass is just as real a Latin letter ...
in short, all of physics is as real as a series of mathematical signs...

You can detect electrons in a detector. You cannot detect virtual particles in a detector.

So Feynman lost a lot of time to identify arrows as fermions, wavy lines as photons and so on .. a picturesque symbolism just to make a tattoo ... who knows, maybe his car, though as I read, had drawn them on his car ...

Your sarcasm doesn't help. Feynman invented calculation tools. Those tools are useful. He did not discover new particles, he just found a much better way to describe existing particles and do the calculations.

 

[vanhees71]

So Feynman lost a lot of time to identify arrows as fermions, wavy lines as photons and so on .. a picturesque symbolism just to make a tattoo ... who knows, maybe his car, though as I read, had drawn them on his car ...

How do you come to this conclusion? Among all the ingenious ideas by Feynman his diagrams are among his most important. Without Feynman diagrams, I'm pretty sure we'd not have been able to use QFT to describe all known elementary particles in such a detailed way as is now represented by the Standard Model, let alone the solution of the difficult problem of renormalization. Last but not least the diagram technique is nowadays used not only in particle physics but also in any other field using QFT methods as in condensed-matter physics etc.

 

[weirdoguy]

So Feynman lost a lot of time to identify arrows as fermions, wavy lines as photons and so on

Your attitude is like "I know better then working physicists do!" but most of the things that you say are just common misconceptions and it's really quite easy to check their fallacy. How many academic courses on QM and QFT have you taken? How many advanced book have you read? It seems to me that you base your knowledge only on pop-sci books and stuff, and that is not a good basis for your sarcastic attitude. Show us some math that justifies it. Or tell us in which textbook we'll find information that virtual particles are as real as electrons. If you really did take any serious course on QM/QFT you'd already know what virtual particles are (Feynman certainly did), or that particle-wave duality is not part of modern QT.

 

[ftr]

I think you all misunderstood what Karolus was saying. He is certainly not against Feynman since his picture(playing Samba, whatever) is his Avatar.

English can be tricky when it comes to indirect talk. He was trying to say ( I think) that the term is and has been widely used and there is probably good reason, although the math is the same for QED, but Casimir controversy and multiple definitions of vacuum do make things confusing.

 

[rkastner]

Hello, I appreciate your disambiguation of the issue of stability from that of virtual quanta. However, I have to point out that your argument against the ontological reality of virtual quanta doesn't work. You say:
"That virtual particles transmit the fundamental forces proves the ”existence” of virtual particles in the eyes of their afficionados. But since they lack states (multiparticle states are always composed of on-shell particles only), they lack reality in any meaningful sense. States involving virtual particles cannot be created for lack of corresponding creation operators in the theory. Thus they cannot cause anything or interact with anything."
Now, I am not an 'aficionado' of virtual quanta. I have no particular need for them to be real. Maybe they're not. But it seems to me that dismissing the reality of an entity simply because there is not a Hilbert (or Fock) space state attribution for that entity is a misplaced dependence on a particular sort of theoretical description to dictate what can be considered real. You acknowledge that forces are mediated by off-shell quanta, and there certainly is a theoretical description of such objects (the propagator)--it's just not a Hilbert Space description. So how can it make sense to say these things don't exist, when they convey forces that can be empirically observed,? Why should a Hilbert space state attribution be a requirement for reality that trumps the fact that these entities mediate empirically observable forces?

 

[PeterDonis]

these entities mediate empirically observable forces

We don't know that virtual particles mediate empirically observable forces. We know that those forces exist because they are empirically observable, but our empirical observations don't tell us that virtual particles mediate the forces.

 

[rkastner]

No, there is no disagreement around whether virtual particles mediate the forces. This is part of the theory--forces are mediated by the off-shell propagators. The original poster acknowledged this when he said "That virtual particles transmit the fundamental forces.." So this is not under dispute. What he's disputing is that we should take virtual particles as real, not whether they mediate forces. He already admits that they do. If he were doubting the theory, he would have said so. Instead, he points to an aspect of the theory --its on-shell states--to argue that virtual particles are not real. So this is not about whether we can know that they exist based on empirical issues, as you express. It's about disqualifying virtual particles for reality based on the kind of theoretical description applicable to them.
I should add that disqualifying an entity's reality based on the fact that it is not directly observable is a mistake. This is what Ernst Mach did with Ludwig Boltzmann's atoms. Clearly, Boltzmann was right. We indirectly observe the results of the mediation of forces by virtual quanta. So it makes no sense to claim that they are not real just because they aren't on-shell. We would have no measurable forces without them!

 

[PeterDonis]

there is no disagreement around whether virtual particles mediate the forces. This is part of the theory--forces are mediated by the off-shell propagators

In one particular theoretical model (perturbation theory), yes. But that is not the only theoretical model for these forces. As the Insights article that is the subject of this comment thread points out, in non-perturbative QFT virtual particles do not appear at all. And perturbation theory is only an approximation to the non-perturbative theory anyway; we use it in cases where we can't compute the non-perturbative theory exactly so we have to fall back on an approximation.

The original poster acknowledged this when he said "That virtual particles transmit the fundamental forces.."

Where did he say that? Quoting out of context is not helpful to the discussion.

 

[rkastner]

I included a more lengthy quote in my original post. It's in his insight article "Misconceptions About Virtual Particles." Here's the quote I originally included: "That virtual particles transmit the fundamental forces proves the ”existence” of virtual particles in the eyes of their afficionados. But since they lack states (multiparticle states are always composed of on-shell particles only), they lack reality in any meaningful sense. States involving virtual particles cannot be created for lack of corresponding creation operators in the theory. Thus they cannot cause anything or interact with anything."
His only argument here against the physical reality of virtual particles (really, whatever is described by propagators) is that they are off-shell. All I'm saying here is that if he accepts that a sound theory describes forces as mediated by propagators, and that one can detect the effects of forces, it makes no sense to say that what the propagators describe is not physically real.

 

[PeterDonis]

His only argument here against the physical reality of virtual particles (really, whatever is described by propagators) is that they are off-shell.

That's the argument he makes in that particular quote. But in the article, he also makes the argument that non-perturbative QFT does not include virtual particles at all.

Also, when he says "that virtual particles transmit the fundamental forces proves the 'existence' of virtual particles in the eyes of their aficionados", he is describing the aficionados' point of view; he is not unequivocally agreeing with it. Much of the rest of the article, in fact, is devoted to showing how the phrase "virtual particles transmit the fundamental forces" is not actually a description of "real physics", but just a convenient heuristic story that should not be taken too seriously. So you should be very careful about laying too much stress on that particular phrase.

 

[A. Neumaier]

It's in his insight article "Misconceptions About Virtual Particles." Here's the quote I originally included: "That virtual particles transmit the fundamental forces proves the ”existence” of virtual particles in the eyes of their afficionados. But since they lack states (multiparticle states are always composed of on-shell particles only), they lack reality in any meaningful sense. States involving virtual particles cannot be created for lack of corresponding creation operators in the theory. Thus they cannot cause anything or interact with anything."
His only argument here against the physical reality of virtual particles (really, whatever is described by propagators) is that they are off-shell. All I'm saying here is that if he accepts that a sound theory describes forces as mediated by propagators, and that one can detect the effects of forces, it makes no sense to say that what the propagators describe is not physically real.

when he says "that virtual particles transmit the fundamental forces proves the 'existence' of virtual particles in the eyes of their aficionados", he is describing the aficionados' point of view; he is not unequivocally agreeing with it.

Indeed, I am not at all agreeing with it, and say in this very quote why. Everything we can say about how a particular physical system behaves in time is derived from its state. Thus properties not encoded in the state can in principle not be observed or even theoretically checked for their validity. The main article on Misconceptions about Virtual Particles explains this in much more detail.

To avoid in the future your kind of misunderstanding, I rephrased in the quoted Insight article the first sentence of the quoted statement to

That Feynman diagrams display virtual particles ''transmitting'' the fundamental forces proves the ''existence'' of virtual particles in the eyes of their afficionados.

 

[Tendex]

It appears to me that here the classical stance about particles instead of the quantum field view is being used to create an artificial debate about the "existence" of particles whether "real" or "virtual". In relativistic quantum field theory the concept of quantum field is stressed instead since there is no particle probability conserved in the same sense as there was for wave functions in non-relativistic quantum mechanics and clicks of detectors refer to excitations of the field and don't have a clear cut identification with "particles" even though the term has unfortunately stuck. The number of particles is not conserved and detections and measurements are not equivalent to "particles" in the classical sense, whether one calls them "real" or "virtual".
Detections' relativistic causality is not preserved using "particles" states but commutators(that vanish for operators at spacelike separation) according to quantum canonical commutation relations, so the argument using states is quite irrelevant here. And all this refers to free quantum fields which are the fundamental bricks with which any QFT is built so it doesn't have anything to do with perturbative versus non-perturbative math(notwithstanding that all this is of course very important to the perturbative S-matrix construction). By the way as of now there exists no non-perturbative relativistic QFT in physical 4-space so I'm not sure why is it being mentioned at all.
Summarizing, this debate is addressing a non-issue and doing it introducing wrong information as it insists on the "existence" of "real particles" suspiciously similar to classical "billiard" particles(which ignores concepts that appear in all QFT texts) when the fundamental concept in RQFT is that of the quantum field that uses relativistic concepts of measurements/detections rather than that of single particles(whose number is not even conserved already for free fields).

 

[A. Neumaier]

It appears to me that here the classical stance about particles instead of the quantum field view is being used to create an artificial debate about the "existence" of particles whether "real" or "virtual".

Nothing in the article assumes classical systems; everything is about the standard formalism for describing quantum particles. These appear even in QFT to describe asymptotic scattering states. The asymptotic description is valid once the distances are mesoscopic, i.e., before and after collisions.

During interactions, the particle picture breaks down completely. It cannot be used to justify virtual particles as agents in what happens.

The number of particles is not conserved

Nothing in the article assumes a conservation law for particle number.

there exists no non-perturbative relativistic QFT in physical 4-space

The frequently used resummation of infinitely many diagrams and renormlization group techniques are non-perturbative feature; so are lattice calculations. That no mathematically rigorous existence proof exists has no impact at all on the very broad research on nonperturbative aspects of QFT.

Thus all your comments are inappropriate.

 

[Tendex]

Nothing in the article assumes classical systems; everything is about the standard formalism for describing quantum particles. These appear even in QFT to describe asymptotic scattering states. The asymptotic description is valid once the distances are mesoscopic, i.e., before and after collisions.

Asymptotic states are mathematical objects as "real" or not as propagators(VEV of time-ordered products which is the math object usually associated to the "virtual particle" concept by field theorists that use that unfortunate terminology)

During interactions, the particle picture breaks down completely. It cannot be used to justify virtual particles as agents in what happens.

I don't know who tries to justify such nonsense as stated. As I said my considerations apply already for free complex scalar quantum fields. I just don't know why certain mathematical abstractions used to obtain certain results seem more "existent" or "real" than others to you. Math objects are math objects, makes no sense to say that an state at future infinity is more real than a vacuum expectation value of time-ordered product. Certainly all the mathematical machinery including particularly the Feynman propagators is needed to justify observations within QFT. The fact that you seem to like better some mathematical objects than others according to some ill defined philosophy of yours is irrelevant here.

Nothing in the article assumes a conservation law for particle number.

Your use of quantum states to justify your philosophy about notions usually considered in this site as outside physics, like reality and existence suggested to me that you are considering only states with fixed numbers of particles when already for quantized free Klein-Gordon complex scalar fields this is untenable.

The frequently used resummation of infinitely many diagrams and renormlization group techniques are non-perturbative feature; so are lattice calculations. That no mathematically rigorous existence proof exists has no impact at all on the very broad research on nonperturbative aspects of QFT.

That a broad research for a mathematically valid non-perturbative theory is ongoing just goes to restate what I wrote about its inexistence, so your reply is not adding anything to my correct statement.

Thus all your comments are inappropriate.

I don't see why. What I think is inappropriate in a physics discussion is introducing cheap philosophical opinions about what "exists" means or about what's "real" disguised as science while apparently nobody else is allowed to do it. More so when it is done ignoring what the causality of measuremnts/detections means in RQFT

 

[A. Neumaier]

I just don't know why certain mathematical abstractions used to obtain certain results seem more "existent" or "real" than others to you.

Well, I gave a clear rationale: To be able to talk about anything in a quantitative way one must at least be able to calculate probabilities for it. Thus the ability to calculate probabilities (in principle) is a suitable criterion for distinguishing the real from the purely conceptual. That's why the state is the key to assign reality, whether to particles or to fields.

What is regarded as real by everyone (e.g., macroscopic objects, unstable atoms, particles colliding, the electromagnetic field) clearly has states determining what is observable about it (e.g., expectation values, decay probabilities, reaction cross sections, linear response).

On the other hand, virtual particles lack all this. For example, to assign to them existence for a short time (how short?) is purely fictitional, and cannot be backed up by any calculation.

That a broad research for a mathematically valid non-perturbative theory is ongoing just goes to restate what I wrote about its inexistence

It shows its existence. Approximate nonperturbative results are still nonperturbative.

If you only count as physics what is rigorously and exactly established, very little of the large edifice of physics remains.

 

[Tendex]

Well, I gave a clear rationale: To be able to talk about anything in a quantitative way one must at least be able to calculate probabilities for it. Thus the ability to calculate probabilities (in principle) is a suitable criterion for distinguishing the real from the purely conceptual. That's why the state is the key to assign reality, whether to particles or to fields.

What is regarded as real by everyone (e.g., macroscopic objects, unstable atoms, particles colliding, the electromagnetic field) clearly has states determining what is observable about it (e.g., expectation values, decay probabilities, reaction cross sections, linear response).

On the other hand, virtual particles lack all this. For example, to assign to them existence for a short time (how short?) is purely fictitional, and cannot be backed up by any calculation.

You are again using vague philosophical distinctions of what is real or not real that are not accepted in mathematical physics discussions , what is your mathematical definition of "virtual particle" for a quantized KG free field? Is it not related to the mathematical conditions(causal propagators) that allow to use them to obtain vacuum expectation values?

It shows its existence. Approximate nonperturbative results are still nonperturbative.

The existence of "approximate nonperturbative results" whatever that means or a research program to obtain them is not what I talked about, I mentioned a mathematically valid nonperturbative theory, which is inexistent at the moment. Why play word games to avoid such true and simple statement?

 

[A. Neumaier]

what is your mathematical definition of "virtual particle" for a quantized KG free field?

An internal line in a graph depicting a Feynman diagram. It has no properties except for the properties a labelled edge in any graph has: two end vertices and a label. Everything else about it is fiction.

I mentioned a mathematically valid nonperturbative theory, which is inexistent at the moment.

Since nothing in elementary particle physics is covered by a mathematically valid nonperturbative theory, the latter (or its nonexistence) cannot be used to argue about conceptual issues in elementary particle physics.

 

[Tendex]

An internal line in a graph depicting a Feynman diagram. It has no properties except for the properties a labelled edge in any graph has: two end vertices and a label. Everything else about it is fiction.

A Feynman diagram is just a pedagogical graphic aid to teach perturbation theory in QFT. A calculational tool. I see no point splitting hairs about what parts of a didactic graph are more or less fictitious, unless it can be traced to some actual conceptual parts of the actual theory that are well defined like free field QFT which you refuse to acknowledge.

Since nothing in elementary particle physics is covered by a mathematically valid nonperturbative theory, the latter (or its nonexistence) cannot be used to argue about conceptual issues in elementary particle physics.

Right. See the first instance I mentioned it, it was to wonder why another poster used it as argument.

 

[A. Neumaier]

A calculational tool.

Yes, this is what the article says it is. Not something real. It is of the same nature as the coefficient of $x^2$ in a power series expansion used to calculate real exponential growth, where nobody claims that it mediates this growth, just because it can be used to calculate it.

I see no point splitting hairs about what parts of a didactic graph are more or less fictitious.

Then why do you split hairs in your comments on my article?

I wrote this Insight article since many stories for lay people give far more reality to virtual particles than they can ever have. They talk about them as if they were entities with well-defined though unobservable dynamical properties, just because they are useful to represent some integrals used to calculate observable things. This is misleading nonsense.

 

[Tendex]

Then why do you split hairs in your comments on my article?

You forgot to quote the complete sentence, it continued with something like "unless it can be traced to the free field theory", but you also forgot my second question: isn't the internal line of a Feynman diagram representing a Feynman propagator?, because if it is so it can be traced to the causal propagator that can be already seen in complex scalar free qft, are you also claiming either yourself or in your article that such propagator is "non-existent" misleading nonsense? Or is it only when represented as an internal line of Feynman diagram?

 

[A. Neumaier]

"unless it can be traced to the free field theory"

Internal lines cannot be traced to the free field theory. They represent a factor in a formal (mathematically ill-defined) integral expression relevant for the interacting theory, not to the free theory. That the factor is a free Feynman propagator doesn't give a deeper physical meaning to the internal line. It rather emphasizes that it is an artifact of expanding around a nonphysical free field.

isn't the internal line of a Feynman diagram representing a Feynman propagator?

It represents what I just explained. But this representation does not imply anything significant. Just as representing a city on a globe by a dot labeled with a name does not make the dot have more properties than the name of the city and the coordinates on the globe.

On the other hand, the Feynman propagator of an interacting quantum field - the object that can be equipped with a physical meaning - is a nonperturbative object, not existing in your rigor mortis philosophy. The free Feynman propagator exists but is physically meaningless.

In its perturbative approximation, the physical Feynman propagator is a weighted asymptotic sum of infinitely many terms, each one given by a complete Feynman diagram, and each one evaluating to infinity if it contains loops. Only the complete sum of all terms with a given number of loops can be given a numerical meaning after renormalization. But the sum over all loops diverges. Thus any physical meaning is very far removed from the internal line picture.

To extract high quality approximations one needs nontrivial partial resummation tricks - all based on assuming the nonperturbative theory to exist. This is needed already to see that the Feynman propagator has poles defining the physical particle mass, and hence needed to make sense out of the standard renormalization conditions.

Without assuming that the nonperturbative theory exists (even though one cannot prove it rigorously at the moment. neither can it be disproved), nothing of interest can be done in quantum field theory. One cannot even get started: Already the derivation of the Feynman rules assume the existence of the nonperturbative theory!

 

[Tendex]

The free Feynman propagator exists but is physically meaningless.

You cannot construct the interacting Feynman propagator without the free one in the same way you cannot construct interacting QFTs without free QFTs. I do believe this is physically meaninful, but I admit you already have confused me enough with your strange use of "existence" and "physical" as conveniently flexible terms, I thought I had gathered you linked "existence" to some kind of "physical" meaning but nope.

 

[A. Neumaier]

You cannot construct the interacting Feynman propagator without the free one in the same way you cannot construct interacting QFTs without free QFTs.

You with your rigor mortis standards can construct neither the interacting Feynman propagator nor interacting QFTs. Thus you cannot even begin writing down the perturbation series for it - which motivated Feynman diagrams and internal lines!

But all books on relativistic QFT assume both and construct practically very useful approximations for both - it is the only reason books on relativistic QFT exist.

I thought I had gathered you linked "existence" to some kind of "physical" meaning but nope.

I linked nonexistence to lack of physical meaning and existence to states that allow one to make quantitiative statements.

 

[Tendex]

You with your rigor mortis standards can construct neither the interacting Feynman propagator nor interacting QFTs. Thus you cannot even begin writing down the perturbation series for it - which motivated Feynman diagrams and internal lines!

But all books on relativistic QFT assume both and construct practically very useful approximations for both - it is the only reason books on relativistic QFT exist.

Please avoid ad hominem attacks, they only reflect nervousness/insecurity. I am obviously not saying that interacting QFTs can't be assumed or constructed, that's just a straw man cop out.
I simply used a trivial enough statementent, that mathematically the interacting QFTs are built from free QFTs, i.e. in this case that an internal line is mathematically a free Feynman propagator so in this, trivial if you want, sense it can be traced to it, and since you can't contradict it directly without some degree of ridicule you resort to a straw man.

I linked nonexistence to lack of physical meaning and existence to states that allow one to make quantitiative statements.

This is in contradiction with the sentence I quoted in my previous post where you link existence to lack of physical meaning instead.

 

[A. Neumaier]

Please avoid ad hominem attacks, they only reflect nervousness/insecurity.

I am neither nervous nor insecure, and didn't attack you personally but only your insistence on a for the topic under discussion inappropriate amount of rigor.

I simply used a trivial enough statementent, that mathematically the interacting QFTs are built from free QFTs,

Now you use 'mahematical' without the rigor mortis setting, in its formal meaning appropriate for quantum field theory.

Mathematically in this formal sense, interacting QFTs are not built from free QFTs, but can be built from free QFTs. They can also be built from lattice approximations leading to Euclidean formulations without any Feynman diagrams, Schwinger-Dyson equations with completely different diagrams, the Schwinger-Keldysh closed time path approach which gives the physical (i.e., interacting) propagators without any detour over free fields, etc.. Their conceptual definition, which gives rise to all these approaches, is independent of any of these constructive ways to get approximations.

i.e. in this case that an internal line is mathematically a free Feynman propagator

It represents a free Feynman propagator. This is quite different from being a free Feynman propagator. Moreover, as concepts from a noninteracting theory, the latter have no physical meaning, so one cannot derive alleged physical properties of virtual particles from them.

 

[Tendex]

Mathematically, nteracting QFTs are not built from free QFTs, but can be built from free QFTs.They also can be built from lattice approximations leading to Euclidean formulations without any Feynman diagrams,

The context is relativistic QFT so I'm not referring to lattices here.

Schwinger-Dyson equations with completely different diagrams,

equivalent to Feynman's as Dyson showed.

the Schwinger-Keldysh closed time path approach which gives the propagators without any detour over free fields, etc..

Not familiar with this approach but I guess it will have some kind of time-ordering which is the key feature of the free Feynman propagator.

the latter have no physical meaning, so one cannot derive physical properties of virtual particles from them.

Mathematical objects like contour integrals have no physical properties that I know of.Anyway, since you mentioned QFT textbooks I'll quote a popular one, Peskin&Schroeder page 31:"the formalism we have developed is extremely important, since the free theory forms the basis for doing perturbative calculations in the interacting theory."

 

[A. Neumaier]

The context is relativistic QFT so I'm not referring to lattices here.

But I am. The Osterwalder-Schrader theorem on which Euclidean field theory is based, is relativistic. Extrapolated lattice QCD uses this, hence is relativistic too. It predicts meson and baryon masses to 5%, wheras nonrelativistic approaches only work for hadrons build from heavy quarks.

equivalent to Feynman's as Dyson showed.

Only in one direction - if you treat Schwinger-Dyson equations in perturbation theory one recovers standard perturbation theory. One cannot go from traditional perturbation theory to Schwinger-Dyson equations.

Not familiar with this approach but I guess it will have some kind of time-ordering which is the key feature of the free Feynman propagator.

Sharing a simple property (also shared by the interacting Feynman propagator) does not mean that there are relevant relations. Free Feynman propagators never appear in the CTP approach., only interacting ones.

Mathematical objects like contour integrals have no physical properties that I know of.

What has this to do with our arguments?

Peskin&Schroeder page 31:"the formalism we have developed is extremely important, since the free theory forms the basis for doing perturbative calculations in the interacting theory."

Yes, for the perturbative way of building QFTs. But not for the other ways mentioned.