In physics, asymptotic freedom is the property of some gauge theories in which the interaction between the particles, such as quarks, becomes arbitrarily weak at ever shorter distances, i. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations In Physics, a quark (kwɔrk kwɑːk or kwɑːrk is a type of Subatomic particle. e. length scales that asymptotically converge to zero (or, equivalently, energy scales that become arbitrarily large). In Physics, length scale is a particular Length or Distance determined with the precision of one order (or a few orders of magnitude An asymptote of a real-valued function y=f(x is a curve which describes the behavior of f as either x or y goes to infinity In Physics, length scale is a particular Length or Distance determined with the precision of one order (or a few orders of magnitude

Contents 1 Discovery 2 Screening and antiscreening 3 Calculating asymptotic freedom 4 See also 5 External links 6 References

Discovery

Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the interactions of quarks and gluons which was discovered in 1973 by David Gross and Frank Wilczek, and by David Politzer. Quantum chromodynamics (abbreviated as QCD is a theory of the Strong interaction ( color force a Fundamental force describing the interactions of the In quantum field theory (QFT the forces between particles are mediated by other particles Gluons ( Glue and the suffix -on) are Elementary particles that cause Quarks to interact and are indirectly responsible for the David Jonathan Gross (born February 19, 1941 in Washington DC Frank Anthony Wilczek (born May 15, 1951) is an American theoretical physicist and Nobel laureate. Hugh David Politzer (born 31 August 1949) is an American theoretical physicist. Although these authors were the first to understand the physical relevance to the strong interactions, in 1969 Iosif Khriplovich discovered asymptotic freedom in the SU(2) gauge theory as a mathematical curiosity, and Gerardus 't Hooft in 1972 also noted the effect but did not publish. Iosif Benzionovich Khriplovich (Иосиф Бенционович Хриплович (1937 &ndash) is a Theoretical physicist who has made deep contributions in Quantum Gerardus 't Hooft (xeːrɑrt ət hoːft (born July 5, 1946, Den Helder) is a professor in Theoretical physics at Utrecht University For their discovery, Gross, Wilczek and Politzer were awarded the Nobel Prize in Physics in 2004. The Nobel Prize in Physics (Nobelpriset i fysik is awarded once a year by the Royal Swedish Academy of Sciences.

Asymptotic freedom implies that in high-energy scattering the quarks move within nucleons, such as the neutron and proton, mostly as free non-interacting particles. Scattering is a general physical process whereby some forms of Radiation, such as Light, Sound or moving particles for example are forced to deviate from In Physics a nucleon is a collective name for two Baryons the Neutron and the Proton. This article is a discussion of neutrons in general For the specific case of a neutron found outside the nucleus see Free neutron. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive It allows physicists to calculate the cross sections of various events in particle physics reliably using parton techniques. In nuclear and Particle physics, the concept of a cross section is used to express the likelihood of interaction between particles Particle physics is a branch of Physics that studies the elementary constituents of Matter and Radiation, and the interactions between them In Particle physics, the parton model was proposed by Richard Feynman in 1969 as a way to analyze high-energy Hadron collisions

The discovery was instrumental in rehabilitating quantum field theory. Prior to 1973, many theorists suspected that field theory was fundamentally inconsistent because the interactions become infinitely strong at short-distances. This phenomenon is usually called a Landau pole, and it defines the smallest length scale that a theory can describe. In Physics, Landau pole is the Energy scale (or the precise value of the Energy) where a Coupling constant (the strength of an interaction of This problem was discovered in quantum electrodynamics, it occurs in field theories of interacting scalars and spinors, and Lehman positivity led many to suspect that it is unavoidable. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics. Asymptotically free theories become weak at short distances, there is no Landau pole, and these quantum field theories are believed to be completely consistent down to any length scale.

While the Standard Model is not entirely asymptotically free, in practice the Landau pole can only be a problem when thinking about the strong interactions. The other interactions are so weak that any inconsistency can only arise at distances shorter than the Planck length, where a field theory description is inadequate anyway. The Planck length, denoted by \scriptstyle\ell_P \, is the unit of Length approximately 1

Screening and antiscreening

The variation in a physical coupling constant under changes of scale can be understood qualitatively as coming from the action of the field on virtual particles carrying the relevant charge. In Physics, a virtual particle is a particle that exists for a limited time and space introducing uncertainty in their energy and momentum due to the Heisenberg Uncertainty The Landau pole behavior of QED is a consequence of screening by virtual charged particle-antiparticle pairs, such as electron-positron pairs, in the vacuum. to most kinds of particles, there is an associated antiparticle with the same Mass and opposite Electric charge. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The positrons or antielectron is the Antiparticle or the Antimatter counterpart of the Electron. In the vicinity of a charge, the vacuum becomes polarized: virtual particles of opposing charge are attracted to the charge, and virtual particles of like charge are repelled. The net effect is to partially cancel out the field at any finite distance. Getting closer and closer to the central charge, one sees less and less of the effect of the vacuum, and the effective charge increases.

In QCD the same thing happens with virtual quark-antiquark pairs; they tend to screen the color charge. In Particle physics, color charge is a property of Quarks and Gluons which are related to their Strong interactions in the context of Quantum However, QCD has an additional wrinkle: its force-carrying particles, the gluons, themselves carry color charge, and in a different manner. Each gluon carries both a color charge and an anti-color magnetic moment. The net effect of polarization of virtual gluons in the vacuum is not to screen the field, but to augment it and affect its color. This is sometimes called antiscreening. Getting closer to a quark diminishes the antiscreening effect of the surrounding virtual gluons, so the contribution of this effect would be to weaken the effective charge with decreasing distance.

Since the virtual quarks and the virtual gluons contribute opposite effects, which effect wins out depends on the number of different kinds, or flavors, of quark. In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their For standard QCD with three colors, as long as there are no more than 16 flavors of quark (not counting the antiquarks separately), antiscreening prevails and the theory is asymptotically free. In fact, there are only 6 known quark flavors.

Calculating asymptotic freedom

Asymptotic freedom can be derived by calculating the beta-function describing the variation of the theory's coupling constant under the renormalization group. In Theoretical physics, specifically Quantum field theory, a beta-function β(g encodes the dependence of a coupling parameter, g on the energy scale In Physics, a coupling constant, usually denoted g, is a number that determines the strength of an Interaction. In Theoretical physics, renormalization group (RG refers to a mathematical apparatus that allows one to investigate the changes of a physical system as one views For sufficiently short distances or large exchanges of momentum (which probe short-distance behavior, roughly because of the inverse relation between a quantum's momentum and De Broglie wavelength), an asymptotically free theory is amenable to perturbation theory calculations using Feynman diagrams. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product In Physics, the de Broglie hypothesis (pronounced /brœj/ as French breuil close to "broy" is the statement that all Matter (any object has a Wave In Quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system Motivation and history When calculating Scattering cross sections in Particle physics, the interaction between particles can be described Such situations are therefore more theoretically tractable than the long-distance, strong-coupling behavior also often present in such theories, which is thought to produce confinement. Color confinement, often called just confinement, is the Physics phenomenon that Color charged particles (such as Quarks cannot be isolated singularly

Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to the interaction of a quark emitting or absorbing a gluon. In non-abelian gauge theories such as QCD, the existence of asymptotic freedom depends on the gauge group and number of flavors of interacting particles. Non-abelian may describe Non-abelian group, in mathematics a group that is not abelian (commutative Non-abelian gauge theory, in physics Gauge theory is a peculiar Quantum field theory where the Lagrangian is invariant under certain transformations In Particle physics, flavour or flavor (see spelling differences) is a Quantum number of Elementary particles related to their To lowest nontrivial order, the beta-function in an SU(N) gauge theory with n_f kinds of quark-like particle is

where α is the theory's equivalent of the fine-structure constant, g² / (4π) in the units favored by particle physicists. Special Unit 2In Mathematics, the special unitary group of degree n, denoted SU( n) is the group of n × n The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing If this function is negative, the theory is asymptotically free. For SU(3), the color charge gauge group of QCD, the theory is therefore asymptotically free if there are 16 or fewer flavors of quarks. In Particle physics, color charge is a property of Quarks and Gluons which are related to their Strong interactions in the context of Quantum

Question: What is N?

Answer: For SU(3) N = 3, and β₁ < 0 gives

See also

• asymptotic safety

External links

• Twenty-five years of asymptotic freedom (by David Gross) (Nobel Prize 2004 for this discovery)

References

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