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{{short description|Class of theories in physics}}

In [[physics]], the term '''bootstrap model''' is used for the class of theories that assume that very general [[consistency]] criteria are sufficient to determine the whole theory completely.

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In [[physics]], theThe term "'''bootstrap model'''" is used for thea class of theories that assume thatuse very general [[consistency]] criteria are sufficient to determine the wholeform of a [[Quantum mechanics|quantum theory]] completelyfrom some assumptions on the spectrum of particles. It is a form of [[S-matrix theory]].

==Overview<!--'Nuclear democracy' redirects here-->==

In the 1960s and '70s, anthe ever-growing list of [[strong interaction|strongly interacting]] particles &mdash; [[meson|mesons]]s and [[baryon|baryons]]s &mdash; causedmade someit clear to physicists that none of these particles are elementary. [[Geoffrey Chew]] and others went so far as to question the distinction between [[compositeComposite particle|composite]] and [[elementary particle|elementary particles]]. In particulars, [[Geoffreyadvocating Chew]] and others advocateda "'''nuclear democracy'''",<!--boldface whichper foresworeWP:R#PLA--> in which the idea that some particles were more elementary than others. was discarded. Instead, they sought to derive as much information as possible about the strong interaction from plausible assumptions about the [[S-matrix]], which describes what happens when particles of any sort collide., an Itapproach isadvocated soby difficult[[Werner toHeisenberg]] findtwo formulasdecades for a nontrivial S-matrix obeying these assumptions that some believed there might be a unique solutionearlier. This led to a bootstrap program often associated with the phrase "the analytic S-matrix".

The reason the program had any hope of success was because of [[Crossing (physics)|crossing]], the principle that the forces between particles are determined by particle exchange. Once the spectrum of particles is known, the force law is known, and this means that the spectrum is constrained to bound states which form through the action of these forces. The simplest way to solve the consistency condition is to postulate a few elementary particles of spin less than or equal to one, and construct the scattering [[Perturbation theory (quantum mechanics)|perturbatively]] through [[Quantum field theory|field theory]], but this method does not allow for composite particles of spin greater than 1 and without the then undiscovered phenomenon of [[Color confinement|confinement]], it is naively inconsistent with the observed Regge behavior of [[hadron]]s.

This bootstrap program had limited success, and it fell out of favor with the rise of [[quantum chromodynamics]]. It is now believed that mesons and baryons are made of elementary particles called [[quarks]] and [[gluons]].

Chew and followers believed that it would be possible to use crossing symmetry and [[Regge theory|Regge behavior]] to formulate a consistent S-matrix for infinitely many particle types. The Regge hypothesis would determine the spectrum, crossing and analyticity would determine the [[scattering amplitude]] (the forces), while [[Unitarity (physics)|unitarity]] would determine the self-consistent quantum corrections in a way analogous to including loops. The only fully successful implementation of the program required another assumption to organize the mathematics of unitarity (the narrow resonance approximation). This meant that all the hadrons were stable particles in the first approximation, so that scattering and decays could be thought of as a perturbation. This allowed a bootstrap model with infinitely many particle types to be constructed like a field theory — the lowest order scattering amplitude should show Regge behavior and unitarity would determine the loop corrections order by order. This is how [[Gabriele Veneziano]] and many others constructed [[string theory]], which remains the only theory constructed from general consistency conditions and mild assumptions on the spectrum.

These are a number of other more successful examples of using general principles to derive specific theories of physics, starting from [[Einstein]]'s 1905 paper on [[special relativity]]. The form of [[general relativity]] is almost entirely specified from general principles including the [[principal of equivalence]]. There has also been partial success in deriving [[Quantum mechanics|quantum theory]] from axioms of [[quantum logic]].

Many in the bootstrap community believed that field theory, which was plagued by problems of definition, was fundamentally inconsistent at high energies. Some believed that there is only one consistent theory which requires infinitely many particle species and whose form can be found by consistency alone. This is nowadays known not to be true, since there are many theories which are nonperturbatively consistent, each with their own S-matrix. Without the narrow-resonance approximation, the bootstrap program did not have a clear expansion parameter, and the consistency equations were often complicated and unwieldy, so that the method had limited success. It fell out of favor with the rise of [[quantum chromodynamics]], which described mesons and baryons in terms of elementary particles called [[quarks]] and [[gluons]].

Bootstrap principles related to the S-matrix also lie behind [[Gabriele Veneziano]]'s early work on [[string theory]], which began as an approach to the strong interaction.

''[[Bootstrapping]]'' here refers to 'pulling oneself up by one's bootstraps,' as particles were surmised to be held together by forces consisting of exchanges of the particles themselves.

More generally, "bootstrapping" refers to any method of reaching higher levels of understanding by building off of lower levels.

In 2017 ''[[Quanta Magazine]]'' published an article in which ''bootstrap'' was said to enable new discoveries in the field of quantum theories. Decades after bootstrap seemed to be forgotten, physicists have discovered novel "bootstrap techniques" that appear to solve many problems. The bootstrap approach is said to be "a powerful tool for understanding more symmetric, perfect theories that, according to experts, serve as 'signposts' or 'building blocks' in the space of all possible quantum field theories".<ref>{{Cite web |last=Wolchover |first=Natalie |date=23 February 2017 |title=Physicists Uncover Geometric 'Theory Space' |url=https://www.quantamagazine.org/using-the-bootstrap-physicists-uncover-geometry-of-theory-space-20170223/ |work=Quanta magazine |access-date=1 October 2021 }}</ref>

==See also==

* [[Tullio Regge]]

* [[Stanley Mandelstam]]

* [[Conformal bootstrap]]

==Notes==

<References/>

== References ==

* G. Chew (1962). ''S-Matrix theory of strong interactions''. New York: W.A. Benjamin.

* D. Kaiser (2002). "Nuclear democracy: Political engagement, pedagogical reform, and particle physics in postwar America." ''Isis'', 93, 229–268.

== Further reading ==

* R. J. Eden, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne, ''The Analytic S-Matrix'', Cambridge U. Press, 1966.

* {{cite magazine |last=Wolchover |first=Natalie |date=9 December 2019 |title=Why the Laws of Physics Are Inevitable |magazine=Quanta Magazine |url=https://www.quantamagazine.org/how-simple-rules-bootstrap-the-laws-of-physics-20191209/}}

[[Category:Particle physicsScattering]]

[[Category:Quantum field theory]]