Bootstrap model
Encyclopedia
In physics
, 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
.
In the 1960s and '70s, the ever-growing list of strongly interacting
particles — meson
s and baryon
s — made it clear to physicists that none of these particles are elementary. Geoffrey Chew
and others went so far as to question the distinction between composite and elementary particle
s, 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 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
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.
More generally, "bootstrapping
" refers to any method of reaching higher understanding by building on lower foundations.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the term bootstrap model is used for a class of theories that use very general consistency
Consistency
Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...
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
S-matrix theory
S-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics.It avoided the notion of space and time by replacing it with abstract mathematical properties of the S-matrix...
.
In the 1960s and '70s, the ever-growing list of strongly interacting
Strong interaction
In particle physics, the strong interaction is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force...
particles — meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s and baryon
Baryon
A baryon is a composite particle made up of three quarks . Baryons and mesons belong to the hadron family, which are the quark-based particles...
s — made it clear to physicists that none of these particles are elementary. Geoffrey Chew
Geoffrey Chew
Geoffrey F. Chew is an American theoretical physicist.He has worked as a professor of physics at the UC Berkeley since 1957 and has been an emeritus since 1991. Chew holds a PhD in theoretical particle physics from the University of Chicago. Between 1950 and 1956, he was a physics faculty member...
and others went so far as to question the distinction between composite and elementary particle
Elementary particle
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not known to be made up of smaller particles. If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which...
s, 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
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
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
Confinement
Confinement may refer to either* Civil confinement for psychiatric patients* Color confinement, the physical principle explaining the non-observation of color charged particles like free quarks* Solitary confinement, a strict form of imprisonment...
, 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
Regge theory
In quantum physics, Regge theory is the study of the analytic properties of scattering as a function of angular momentum, where the angular momentum is not restricted to be an integer but is allowed to take any complex value...
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
Gabriele Veneziano, born in Florence, Italy), is an Italian theoretical physicist and the founder of string theory. . Has spent most of his scientific activities at CERN in Geneva, Switzerland...
and many others, constructed string theory
String theory
String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
, 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
Quantum chromodynamics
In theoretical physics, quantum chromodynamics is a theory of the strong interaction , a fundamental force describing the interactions of the quarks and gluons making up hadrons . It is the study of the SU Yang–Mills theory of color-charged fermions...
, which described mesons and baryons in terms of elementary particles called quarks and gluons.
More generally, "bootstrapping
Bootstrapping
Bootstrapping or booting refers to a group of metaphors that share a common meaning: a self-sustaining process that proceeds without external help....
" refers to any method of reaching higher understanding by building on lower foundations.