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

+ 3 like - 0 dislike

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 in Phenomenology by - (255 points) [ revision history ]

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

2 Answers

+ 6 like - 0 dislike

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 Ron Maimon (7,590 points) [ revision history ]

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.

+ 6 like - 0 dislike

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 Arnold Neumaier (13,959 points) [ revision history ]
edited Aug 29, 2014 by Arnold Neumaier

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. 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.

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

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