# Is "Nuclear Democracy" and "Bootstrapping" the same principle, in Chew's work?

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According most descriptions of Chew's work, he postulated a principle called "Nuclear Democracy" in which there is no distinction between composite and elementary particles. Is this principle the same that the Bootstrap? And, if not, which is the relationship between both ideas?

The answers; I think, should explain what boots is the theory wearing and which straps have such boots got.

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In a QFT, once one forgets about Lagrangians and Hamiltonians and only keep the S-matrix, one has nuclear democracy, as from the S-matrix alone one cannot tell whether an asymptotic particle is elementary or composite. (Indeed, some 1+1D QFTs have the same S-matrix but several Hamiltonian descriptions, and what is elementary and what is composite depends on which description one assumes to be ''the true one''. This is related to bosonization of fermions; see http://www.physicsoverflow.org/22342/solitons-the-paper-quantum-meaning-classical-field-theory?show=22343#a22343 or http://www.physicsoverflow.org/16202 )

The bootstrap is the idea that one can identify the correct S-matrix of elementary particles without knowing an underlying  Lagrangian or Hamiltonian formulation, just from the principles of covariance (leading to a Regge structure of the bound states), unitarity and crossing symmetry.

Thus the bootstrap is closely related to nuclear democracy.

answered Aug 29, 2014 by (14,547 points)
edited Aug 29, 2014

And which one were the opionion of their opponents, who separated particles on composite and elementary? Did they try to make some classification which partricles could consist of which?

Or they meant that all known particles cannot consist of each other, but some of them may consist of something yet unknown (like quarks) and some is fundamental (like leptons)?

@Pavel: The bootstrap was popular only before the advent of gauge theories for the weak and strong interactions. the latter proved to be a much stronger framework for fundamental physics. There particles are deemed elementary if they appear in a renormalizable Lagrangian, and composite otherwise.

@Pavel: The Standard Model answers partially your questions. This is what was accepted in the end. @ArnoldNeumaier: But I disagree with the statement:

There particles are deemed elementary if they appear in a renormalizable Lagrangian, and composite otherwise.

There are no elementary particles even though they appear in a Lagrangian, and this is for a very simple reason - they are interacting with other particles. This interaction is permanent, so we may speak of elementary excitations of compound systems instead. Further simplification like neglecting some essentials lead to nonsense.

As a matter of fact, we observe some processes, which we "identify", "simplify", "axiomatize", etc. as something intact (elementary) entities, but interacting anyway. Observation is a physical process involving a lot of staff and human experience. It is not like imagining mathematically well defined (but thus too poor) entities.

"The opinion of their opponents"  was the following: we must search for better Hamiltonians (P. Dirac).

Of course, it is impossible from physical equations to state is particle elementary (does not consist of other elementary particles) of composite (consist of other elementary particles). You will need some chemical considirations to do that - some investigation on the reactions of particles. I agree with term "identify", or more softer, "classify". Interaction is anyway, and you can have different models to take it in account. But it is better when you approximate motion of composite particle by Hamiltonian for particles of which it consist, is not it?

In my question I mean following:

Now terms elementary and composite lost their initial meaning for physicists. Standard answer is - they all are composite as consist of quarks.

That is natural, as in Standard Model all explainable particles are elementary (consist only from subparticle quarks) and not explainable as well elementary (does not consist of quarks). That is because of initial idea that all particles are similarly elementary (nuclear democracy). In fact, it forbids any composite particles, any "compounds" between particles. And if some particles in Particle Zoo are constructed in that composite way, they anyway is classified as elementary and already is taken in account.

It is interesting what was the vision of opponents to nuclear democracy? What was their opinion? Their names? What did they say in disscussions?

@Arnold Neumaier, By the way, if bosonisation of fermions is concerned, does the thery of collective motion of bosons with fermions exists? I saw something for 1D on lattices. Somebody did calculations on behavior of systems consisting of charged bosons and charged fermions? What it looks like, I wonder...

The problem is that ''a particle cannot decay into other particles'' cannot be taken as definition  of being elementary. Every bound state has this property when isolated, and no particle has this property in a sufficiently energetic environment. This establishes nuclear democracy - it is a theorem in algebraic quantum field theory. But for practical purposes we want to declare some particles as basic and the others as their composites. Doing this on the basis of renormalizable Lagrangians is convenient.

Regarding your last question, the case of 1+1D QFT is special because there the connection between spin and statistics is ambiguous, as shown by the phenomenon of bosonization/fermionization. But this should be discussed in a separate thread, not here.

I am surprised how deep you feel, @Arnold. Yes. That is root of problem. Nuclear reaction are more flexible that chemical. In chemistry, even if we would not be smart enouph to classify elements correctly for several centuries before development of mass-spectrometry, we could still charge molecules and atoms and just collide them with inert gas, like we can do now. And so, we could see real picture, real elements. As nuclei are bonded much stronger that chemical bonds and will not changed. That is not possible for nuclear reactions.

But, @Arnold, even without possibility to detect so, that is not strong logical reason for "nuclear democracy" conclusion. Chemists found out which substances were pure elements and which were compounds of elements prior to mass-spectrometry. That was made by reactions, weights and volumes of its products. The science with "all substances are equally elementary" was alchemy, I am affraid.

And yes, discussion gets offtopic. But it is very interesting. @Arnold, please, mail me to coodan@mail.ru

Chemistry is essentially nonrelativistic (with small relativistic corrections only). That's why we can assume conservation of nuclei and electrons, which is the basis for deciding what are atoms and what are molecules. One cannot do the same on the level of elementary particles.

@Arnold, yes, that true. But you can use experience and succesfull approaches from different level. Even if you have obvious restrictions. Yes. You are on the level where energy is participant of reactions, where particles and energy may be transformed in each other. Nothing similar is on the chemical level. But when you (not obviously) forbid any composites (compounds between particles), you so forbid chemistry. Alchemistry is then only alternative. But why electrons may give such an amount of compounds in chemistry (>100.000.000 known), and to other particles in Particle Zoo it is forbiden? Chemistry is most massive level of fermion interaction, that is true. But some similarity in behavevior would be expectable, would not it?

The point is that on the level of elementary particles, only charges are conserved, not particle numbers; therefore the chemistry analogy breaks down.

@ArnoldNeumaier: In order to speak of charge consevation of something, it is necessary to isolate this something. And this process (of isolating) includes different states of this "something". So this something is not intact, but an inclusive picture of different somethings ;-)

Do you see the difference between math and phys?

@Arnold, that is not so. As a result of nuclear democracy you do not see variants when one particle can consist of other particles - "compounds". That "elementary" particles inside compound will conserve. And compound is just some bonded state of them. In quark model compouns not possilbe - all particles are classified as diquarks and triquarks. Even if some of them in fact consist of other particles, which consist of quarks. That is a result of nuclear democracy. You cannot see compounds from inside of that conception, as if they exist, they already are classified as diquarks and triquarks. Parameters of matrixes already calibrated to expain/predict tendencies. Even if "compounds" and "elements" are mixed.

The way to escape this problem, proven in chemistry for centuries is firstly separate "elementary" from "compounds", then consider only "elementary", find the tendencies  for them (it keeps less number of "quarks" or quantum numbers) and after this classify "compounds" and find the tendencies for them. After all, it is simpler, as tendencies may be different for "elementary" and "compounds". It is forbidden by nuclear democracy. As if all are equally elementary, then no compounds between elementary is allowed.

For example, even if (ohh, nightmare) neutron is "compound" (consisting of proton and something) you will not see it from inside of that conception, as it is already classified in it as "elementary" (consisting only of 3 quarks). Because of nuclear democracy.

That is like equality of people in Soviet-style: all rich were forbiden, and all poor get equally poor.

@Vladimir Kalitvianski, yes, inclusive is correct word, but that looks like some "fractal" inclusive, may be. To be correct, it is some concept from combinatorics. To have in one set ordinary elements and combinations of that elements included and expect that all are ordinary. So, that kind of combinatorics is forbiden by nuclear democracy from math point of view. You are welcome to mail discussion too, if you like coodan@mail.ru   :)

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They are pretty much the same. The principle of "Nuclear democracy" is just that all the hadrons are equally composite, and if you want to make a theory for them, you can't select a few of them (like, say, the Proton, Neutron, and Lambda, as Sakata suggested) and say that these are fundamental particles in a Lagrangian, and all the rest are built as bound states of these fundamental particles, because you might as well have said it about any others.

The Bootstrap was an attempt to make a theory by postulating an S-matrix for the Regge trajectories of the hadrons. The idea here is that you use the principles of S-matrix unitarity and analyticity, plus the requirement of Regge behavior for the exchange of a family of related particles, to produce a theory where you don't have any fundamental fields and you don't have any Lagrangian. All you have are the analogs of Feynman diagrams for the exchange of Regge trajectories.

There are also phenomenonlogical bootstraps, where you start with some strongly interacting particles, and try to reproduce the scattering and produce others as bound states, and then somehow try to close the system, but this is a more difficult and essentially fruitless idea, which is either equivalent to building up an effective field theory, or else it's equivalent to nothing, depending on who was doing it.

But the idea of building up a theory of exchanges of Regge trajectories can be done, in essentially one way, or rather, at least we only have exactly one example of a consistent bootstrap, and that's string theory. Maybe there are other unrelated bootstraps out there, but nobody found any.

answered Aug 29, 2014 by (7,720 points)

I believed that the bootstrap was not only that all the hadrons are equally composite, but that they are composite of themselves. Is it?

They are composite with no fundamental constituents in this view, so you can call them "composites of themselves". In practice, that just means no field theory Lagrangian, no fundamental fields.

Did any supporters of composite/elementary point of vies suggest neutron as possible composite particle, or neutron had strong aliby to be fundamental?

There is an interview on YouTube with Gell-Mann.

He relates the history (his history) of bootstrap and democracy (episode 48).

Is it like Star Wars? )))

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