# 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 (14,537 points)
edited Aug 29, 2014

@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.

@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.

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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