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

+ 4 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 28, 2014 in Phenomenology by - (260 points) [ revision history ]

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

2 Answers

+ 7 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 (15,787 points) [ revision history ]
edited Aug 29, 2014 by Arnold Neumaier
Most voted comments show all comments

@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. 

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   :)

Most recent comments show all comments

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?

+ 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 28, 2014 by Ron Maimon (7,720 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.

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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