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
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.
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
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
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
and many others,
constructed string theory, which remains the only theory constructed
from general consistency conditions and mild assumptions on the
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.
G. Chew (1962). S-Matrix theory of strong interactions. New York: W.A.
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