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Parouse.com

The term "bootstrap model" is used for a class of theories that use
very general consistency criteria to determine the form of a quantum
theory from some assumptions on the spectrum of particles. It is a
form of
**S-matrix** theory.
Overview[edit]
In the 1960s and '70s, the ever-growing list of strongly interacting
particles — mesons and baryons — made it clear to physicists that
none of these particles are elementary.
**Geoffrey Chew**

Geoffrey Chew and others went so far as to question the distinction between composite and elementary particles, advocating a "nuclear democracy" 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 approach advocated by**Werner Heisenberg**

Werner Heisenberg two decades earlier. The reason the program had any hope of success was because of 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 perturbatively through field theory, but this method does not allow for composite particles of spin greater than 1 and without the then undiscovered phenomenon of confinement, it is naively inconsistent with the observed Regge behavior of hadrons. Chew and followers believed that it would be possible to use crossing symmetry and 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 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**

Gabriele Veneziano and many others, constructed string theory, which remains the only theory constructed from general consistency conditions and mild assumptions on the spectrum. 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. "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. See also[edit]

Geoffrey Chew and others went so far as to question the distinction between composite and elementary particles, advocating a "nuclear democracy" 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 approach advocated by

Werner Heisenberg two decades earlier. The reason the program had any hope of success was because of 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 perturbatively through field theory, but this method does not allow for composite particles of spin greater than 1 and without the then undiscovered phenomenon of confinement, it is naively inconsistent with the observed Regge behavior of hadrons. Chew and followers believed that it would be possible to use crossing symmetry and Regge behavior to formulate a consistent

Gabriele Veneziano and many others, constructed string theory, which remains the only theory constructed from general consistency conditions and mild assumptions on the spectrum. 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. "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. See also[edit]

Tullio Regge Stanley Mandelstam Conformal bootstrap

References[edit]

G. Chew (1962). S-Matrix theory of strong interactions. New York: W.A. Benjamin. R. J. Eden, P. V. Landshoff, D. I. Olive and J. C. Polkinghorne (1966). The Analytic S-Matrix. Cambridge U. Press. 1966. D. Kaiser (2002). "Nuclear democracy: Political engagement, pedagogical reform, and particle physics in postwar America." Is