# 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?

asked Aug 29, 2014

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 (12,890 points)
edited Aug 29, 2014
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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 (7,535 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.

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