Asymptotic freedom

[7] Prior to 1973, many theorists suspected that field theory was fundamentally inconsistent because the interactions become infinitely strong at short distances.This problem was discovered in field theories of interacting scalars and spinors, including quantum electrodynamics (QED), and Lehmann positivity led many to suspect that it is unavoidable.[10] 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.The net effect of polarization of virtual gluons in the vacuum is not to screen the field but to augment it and change its color.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.Asymptotic freedom can be derived by calculating the beta function describing the variation of the theory's coupling constant under the renormalization group.For sufficiently short distances or large exchanges of momentum (which probe short-distance behavior, roughly because of the inverse relationship between a quantum's momentum and De Broglie wavelength), an asymptotically free theory is amenable to perturbation theory calculations using Feynman diagrams.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.Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to the interaction of a quark emitting or absorbing a gluon.gives Thus for SU(3), the color charge gauge group of QCD, the theory is asymptotically free if there are 16 or fewer flavors of quarks.Finally, one can find theories that are asymptotically free and reduce to the full Standard Model of electromagnetic, weak and strong forces at low enough energies.