Are hadrons quasiparticles?

[Demystifier]

First, let me ask moderators not to move this thread to the High Energy, Nuclear, Particle Physics forum, because I am interested in hadrons from a wider perspective, especially from the perspective of condensed-matter QFT.

A hadron (e.g. proton, neutron, or pi-meson) is a complicated mixture involving 2 or 3 quarks and a sea of gluons. From perspective of non-perturbative QCD, one would say that it is a bound state of quarks and gluons. But how about condensed-matter perspective? Can we say that hadron is a collective particle-like excitation of quark and gluon fields? Or more specifically, can we say that hadron is a quasiparticle in the condensed-matter terminology? If it is not a quasiparticle, then what property of quasiparticles is missing in the case of hadrons?

A wider goal of such questions is to better understand the similarities and differences between QFT concepts in high-energy and condensed-matter physics.

 

[stevendaryl]

A quick look using Google seems to show that people don't use "quasiparticle" to include "composite particle", but I'm not sure if there is a principled reason why not.

 

[A. Neumaier]

is a complicated mixture

no, it is a bound state, not a mixture.

what property of quasiparticles is missing in the case of hadrons?

It has far too few constituents. To define a quasiparticle in the condensed matter sense you need a macroscopic amount of substance.

 

[Demystifier]

It has far too few constituents.

Roughly how many gluons a hadron has?

To define a quasiparticle in the condensed matter sense you need a macroscopic amount of substance.

Why a macroscopic amount of substance is important?

 

[A. Neumaier]

Roughly how many gluons a hadron has?
Why a macroscopic amount of substance is important?

The first question has no answer since gluons are massless; hence there is an unlimited number of very soft gluons (which don't count in a statistical mechanics treatment). One has to sum these up into a coherent state. The contribution of hard gluons (which would count) is small; one can probably even neglect it to a good approximation.

A macroscopic amount of substance is important in order that statistical mechanics (in the usual sense) is applicable. Formally, one has to perform a thermodynamic limit, in which the Bogoliubov transformation that defines the quasiparticles produces a representation inequivalent to the vacuum representation (in which the ordinary particles are defined).

 

[Demystifier]

A macroscopic amount of substance is important in order that statistical mechanics (in the usual sense) is applicable.

Why is it important that statistical mechanics is applicable? Are you saying that quasiparticles only make sense in the context of statistical mechanics?

 

[A. Neumaier]

What would be your definition of a quasiparticle without statistical mechanics?

 

[Demystifier]

What would be your definition of a quasiparticle without statistical mechanics?

A primary example of a quasiparticle I have in mind is a phonon, as described e.g. in Sec. 1.1 of Ben Simons's Concepts in Theoretical Physics which can be freely download here
http://free-ebooks.gr/en/book/concepts-in-theoretical-physics [Broken]

 

[A. Neumaier]

A primary example of a quasiparticle I have in mind is a phonon, as described e.g. in Sec. 1.1 of Ben Simons's Concepts in Theoretical Physics which can be freely download here
http://free-ebooks.gr/en/book/concepts-in-theoretical-physics

The phonon makes sense only in a solid lattice, hence presumes a many-body system in the background.

Of course you may consider relativistic QFT with cutoff as a strongly interacting many-body system of bare particles (a kind of ether) and the vacuum as its ground state. Then all elementary particles (not only the composite ones) become quasiparticles in this picture. The problem is that this picture makes no longer sense if the cutoff is removed.

 

[Demystifier]

The phonon makes sense only in a solid lattice, hence presumes a many-body system in the background.

Why solid? I think there are phonons in fluids too. I agree with the importance of the many-body background, which leads us to the next point ...

Of course you may consider relativistic QFT with cutoff as a strongly interacting many-body system of bare particles (a kind of ether) and the vacuum as its ground state. Then all elementary particles (not only the composite ones) become quasiparticles in this picture.

Yes, that philosophy is much more in the spirit I had in mind. But intuitively, hadron is somehow more "quasi" than quark or gluon, in the sense that it is more "emergent" and less "elementary". I am not sure if such intuition can be made to make more sense.

The problem is that this picture makes no longer sense if the cutoff is removed.

Fine, but QFT without cutoff does not make sense for many other reasons, so let us work with the cutoff all the time.

 

[A. Neumaier]

intuitively, hadron is somehow more "quasi" than quark or gluon, in the sense that it is more "emergent" and less "elementary". I am not sure if such intuition can be made to make more sense.

With a cutoff, the many-body background would be a non-covariant ether consisting of highly interacting bare particles with an interaction that depends heavily on the cutoff.

On this background one can liken elementary bosons to phonons in a solid or fluid, elementary fermions to effective electrons in a conductor, mesons to Cooper pairs in a superconductor, and baryons in a more figurative way to a kind of ''Cooper triples'', since they are dressed versions of single particles, particle pairs, and triples. But I have no idea what one would gain from using this analogy (which apparently was widespread in the 1950s but since then lost ground). Maybe because you want to build a Bohmian mechanics on top of it? But then you have to explain why all the couplings are extremely sensitive to the cutoff!

In practice, it is rather the opposite way, that one wants to liken quasiparticles to particles! Indeed, one works in condensed-matter physics with quasiparticles precisely since these behave somewhat like elementary quantum particles.

 

[Demystifier]

With a cutoff, the many-body background would be a non-covariant ether consisting of highly interacting bare particles with an interaction that depends heavily on the cutoff.

I don't see why would that be a problem.

But I have no idea what one would gain from using this analogy ... Maybe because you want to build a Bohmian mechanics on top of it?

That too, but I have other reasons as well:
http://arxiv.org/abs/1505.04088

 

[atyy]

"quasiparticle method of Weinberg"

http://arxiv.org/abs/hep-ph/9805459v1
"In Weinberg’s quasiparticle approach the bound states are redescribed by elementary particles and, in order not to change the physics of the problem, the potential is modified in such a way that it cannot produce these bound states any longer."

http://arxiv.org/abs/nucl-th/9710073v1

 

[A. Neumaier]

I don't see why would that be a problem.

It is of the same kind as the fine-tuning problem in grand unification. It is not a problem if you treat the interactions as God-given.

 

[A. Neumaier]

"quasiparticle method of Weinberg"

Weinberg's notion of quasiparticles is different from that of condensed matter physics.
One can see this from the abstract of his 1963 paper http://journals.aps.org/pr/abstract/10.1103/PhysRev.131.440 [Broken].

Perturbation theory always works in nonrelativistic scattering theory, unless composite particles are present. By "composite particle" is meant a bound state or resonance, or one that would exist for an interaction of opposite sign; in fact, this provides a precise definition of resonances. It follows that if fictitious elementary particles (quasiparticles) are first introduced to take the place of all composite particles, then perturbation theory can always be used. There are several ways of accomplishing this [...]

 

[atyy]

Weinberg's notion of quasiparticles is different from that of condensed matter physics.
One can see this from the abstract of his 1963 paper Quasiparticles and the Born Series.

I was thinking in the sense that a "quasiparticle" is a particle in the low energy effective theory. Eg. if the electron is emergent, then it is a quasiparticle. So in that sense, Weinberg's quasiparticles are quasiparticles. (I see you said something like this in poist #11.)

 

[A. Neumaier]

I was thinking in the sense that a "quasiparticle" is a particle in the low energy effective theory. Eg. if the electron is emergent, then it is a quasiparticle. So in that sense, Weinberg's quasiparticles are quasiparticles. (I see you said something like this in poist #11.)

Weinberg's paper is not about low energy approximations. He calculates the bound states exactly from a bigger Hilbert space in which free quasiparticles are added artificially to be able to do an improved perturbation theory. The bound statres computed are complicated composites of the original particles and the added quasiparticles. This is very unlike what is done in condensed matter theory.

On the other hand, post #11 assumes from the start that we have a cutoff (in order to be able to define the background), which means working in a truncated Hilbert space and then defines quasiparticles to be the bound states of the truncated description. This is analogous to thedressing of an elecron in condensed matter theory.

Thus the two concepts of quasiparticles go into opposite directions.

 

[Demystifier]

It is of the same kind as the fine-tuning problem in grand unification. It is not a problem if you treat the interactions as God-given.

How else can interactions be given?

 

[A. Neumaier]

How else can interactions be given?

Many people interested in grand unification or string theory believe that a really fundamental theory should have no tunable parameter (except those for which the predictions are fairly insensitive) but be completely determined by symmetry principles. To need the constants to 20 digits relative accuracy to get a prediction accuracy of 2 digits is considered by them as too unnatural for a fundamental theory. This is what is behind the so-called fine-tuning problem.

If one works with a fixed value of cutoff and bare couplings, one has the same problem.

 

[Demystifier]

Many people interested in grand unification or string theory believe that a really fundamental theory should have no tunable parameter (except those for which the predictions are fairly insensitive) but be completely determined by symmetry principles. To need the constants to 20 digits relative accuracy to get a prediction accuracy of 2 digits is considered by them as too unnatural for a fundamental theory. This is what is behind the so-called fine-tuning problem.

If one works with a fixed value of cutoff and bare couplings, one has the same problem.

OK, but I don't think that QFT is fundamental theory. And I am not alone, many high-energy physicists do not think that QFT is fundamental theory. Many (including Weinberg) hold the view that all quantum field theories are only effective theories. Such a view is also implicit in the Wilsonian approach to renormalization (group), which is rather condensed-matter-like in spirit, and yet quite popular among high-energy physicists.

 

[atyy]

OK, but I don't think that QFT is fundamental theory. And I am not alone, many high-energy physicists do not think that QFT is fundamental theory. Many (including Weinberg) hold the view that all quantum field theories are only effective theories. Such a view is also implicit in the Wilsonian approach to renormalization (group), which is rather condensed-matter-like in spirit, and yet quite popular among high-energy physicists.

I think it is explicit in Wilsonian renormalization, since it is with Wilson that non-renormalizable theories like gravity are ok. Wilson is truly condensed matter and HEP in spirit. Wilson was a HEP physicist, but the theory of critical phenomena and the Kondo problem where he first carried out his calculations were condensed matter, but it was clear that the calculations were linked to HEP renormalization calculations.

So HEP is a far superior field of physics, since it saved condensed matter. In contrast, condensed matter physicists only contributed one God particle to HEP.

 

[Demystifier]

Most QFT textbooks promote either high-energy or condensed-matter style of thinking, not both. Those that promote both are quite rare. I think it would be useful to have a list of books that promote both, so here is my (probably incomplete) list of such both-styles-in-one-book textbooks:

Non-free:
- Lancaster and Blundell - QFT fot the Gifted Amateur (very pedagogic)
https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20
- Ziman - Elements of Advanced Quantum Theory (very old - 1969)
https://www.amazon.com/dp/0521099498/?tag=pfamazon01-20
- Padmanabhan - QFT (very new - 2016)
https://www.amazon.com/dp/3319281712/?tag=pfamazon01-20
- Le Bellac - Quantum and Statistical Field Theory
https://www.amazon.com/dp/0198539649/?tag=pfamazon01-20
- Zee - QFT in a Nutshell
https://www.amazon.com/dp/0691140340/?tag=pfamazon01-20
- Umezawa - Advanced Field Theory
https://www.amazon.com/dp/1563960818/?tag=pfamazon01-20

Free:
- Kleinert - Particles and Quantum Fields (very big - more than 1600 pages in the current edition, and frequently updated*)
http://users.physik.fu-berlin.de/~kleinert/b6/psfiles/qft.pdf
- Simons - Concepts in Theoretical Physics (very pedagogic)
http://free-ebooks.gr/en/book/concepts-in-theoretical-physics

Please add any relevant book you know that I might have missed.

--------------------
* Off-topic: For those who like good, big, free and frequently updated textbooks, let me also recommend
- Blau - Lecture Notes on General Relativity (more than 900 pages in the current edition)
http://www.blau.itp.unibe.ch/newlecturesGR.pdf
If "frequently updated" is not the requirement, then the following one also fits
- Mauch - Advanced Mathematical Methods for Scientists and Engineers (more than 2300 pages)
http://physics.bgu.ac.il/~gedalin/Teaching/Mater/am.pdf

 

[atyy]

In a sense, the exposition http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf by 't Hooft is condensed matter in spirit, because he says: "Often, authors forget to mention the first, very important, step in this logical procedure: replace the classical field theory one wishes to quantize by a strictly finite theory. Assuming that physical structures smaller than a certain size will not be important for our considerations, we replace the continuum of three-dimensional space by a discrete but dense lattice of points."

 

[A. Neumaier]

in this logical procedure

In which logical procedure?

 

[Demystifier]

In which logical procedure?

Quantization of a classical field theory.

 

[A. Neumaier]

In a sense, the exposition http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf by 't Hooft is condensed matter in spirit, because he says: "Often, authors forget to mention the first, very important, step in this logical procedure: replace the classical field theory one wishes to quantize by a strictly finite theory. Assuming that physical structures smaller than a certain size will not be important for our considerations, we replace the continuum of three-dimensional space by a discrete but dense lattice of points."

You overestimate the cogency of motivational handwaving arguments.

t'Hooft is self-contradictory when taken literally in his motivations. By the same token he eliminates (on p.13) structures larger than a certain size and imposes periodic boundary conditions to get a strictly finite system. The resulting strictly finite system is then quantized - but it has no longer asymptotic in- and out-states and hence has no well-defined scattering problem. But the latter was his starting point on p.5!

Moreover, on p. 13 he begins the argument by saying ''it is often forgotten how these answers can be derived rigorously'' - but today there is still no rigorous derivation, only the kind of handwaving he presents. Every derivation of the scattering formula of LSZ (which is the true basis of all perturbative QFT calculations) involves a flat Minkowski space-time and a Poincare invariant field theory!

On p.29 he says ''renormalizability requires our theory to be consistent up to the very tiniest distance scales'', meaning tha continuum limit, as otherwise - in a strictly finte system - there is no renormalizability problem at all! And on the next page, p.30, he states ''renormalizability provides the required coherence of our theories'', Thus he explicitly revokes his earlier motivation to be able to get to the heart of the matter. The bulk of the paper, after all the introductory motivational bla bla that you take for gospel has been said, the remaining 40 pages, are about the limiting theory, and the techniques used (e.g., dimensional regularization and topological considerations) assume Poincare invariance. On p.41 he says: ''Unitarity of the S-matrix turns out to be a sensitive criterion to check whether we are performing the continuum limit correctly'' - which makes sense only if the continuum limit is relevant to the standard model - which it indeed is!

Thus t'Hooft's motivational arguments in the first 16 pages cannot be taken literally and have to be interpreted with many grains of salt!

Note that he got his Nobel prize not for work on a strictly finite quantum field theory in the sense he described on p.13 but for showing that quantizing certain (continuum) classical gauge theories with matter and spontaneously broken symmetry - in a construction with infinitely many degrees of freedom! - one obtains (in renormalized perturbation theory) a renormalizable, Poincare-invariant QFT.

This is very far from what he painted in the introductory quarter of the paper for the purpose of simplifying the true (technically correct) situation. Indeed, it is still unknown today whether a strictly finite lattice-based construction has a good infrared (large distance) and ultraviolet (small distance) limit - so at present lattices (and their limits) cannot give a good foundation of the standard model.

By the way, t'Hooft discusses on p.65 the fine-tuning problem as something problematic enough that ''it becomes difficult to believe that it [the standard model] represents the real world'' at high enough energies.

 

[Demystifier]

You overestimate the cogency of motivational handwaving arguments.

Kurt Lewin famously said: "There is nothing so practical as a good theory."
Let me paraphrase him by saying: "There is nothing so convincing as a good hand-waving argument."

 

[A. Neumaier]

There is nothing so convincing as a good hand-waving argument."

Especially if you have several that contradict each other, as in the present case.

 

[Demystifier]

Especially if you have several that contradict each other, as in the present case.

You are right that 't Hooft contradicts himself, but I have a justifying quote for that too:
“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth."
- Niels Bohr

 

[A. Neumaier]

You are right that 't Hooft contradicts himself, but I have a justifying quote for that too:
“The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth."
- Niels Bohr

But physics is about predictive formalisms, not about profound truths. The latter are reserved for the informal interpretation of the formalism.

 

[Demystifier]

But physics is about predictive formalisms, not about profound truths. The latter are reserved for the informal interpretation of the formalism.

To defend 't Hooft I would say that physics is not only about predictive formalism, but also about ideas that justify that formalism. Indeed, the 't Hooft lectures on QFT (as pretty much any other QFT textbook) starts with some heuristic ideas and ends up with some predictive formalism.

 

[A. Neumaier]

To defend 't Hooft I would say that physics is not only about predictive formalism, but also about ideas that justify that formalism. Indeed, the 't Hooft lectures on QFT (as pretty much any other QFT textbook) starts with some heuristic ideas and ends up with some predictive formalism.

Sure, lots of heuristics precedes the formulation of a working model.

The point that I had wanted to make is that atyy's initial quote in post #25 was taken out of context and doesn't make the standard model ''condensed matter in spirit" - it only creates an informal bridge between the two.

 

[Demystifier]

The point that I had wanted to make is that your initial quote in post #25 was taken out of context and doesn't make the standard model ''condensed matter in spirit" - it only creates an informal bridge between the two.

That post was written by atyy, not me. I agree that it only makes an informal bridge.

 

[A. Neumaier]

That post was written by atyy, not me. I agree that it only makes an informal bridge.

corrected.