In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. Usually the Lagrangian or the Hamiltonian of a system can be separated into a kinetic part and an interaction part. The coupling constant determines the strength of the interaction part with respect to the kinetic part, or between two sectors of the interaction part. For example, the electric charge of a particle is a coupling constant.
A coupling constant plays an important role in dynamics. For example, one often sets up hierarchies of approximation based on the importance of various coupling constants. In the motion of a large lump of magnetized iron, the magnetic forces are more important than the gravitational forces because of the relative magnitudes of the coupling constants. However, in classical mechanics one usually makes these decisions directly by comparing forces.
One can probe a quantum field theory at short times or distances by changing the wavelength or momentum, k of the probe one uses. With a high frequency, ie, short time probe, one sees virtual particles taking part in every process. The reason this can happen, seemingly violating the conservation of energy is the uncertainty relation
In quantum field theory, a beta-function β(g) encodes the running of a coupling parameter, g. It is defined by the relation:
If the beta-functions of a quantum field theory vanish, then the theory is scale-invariant.
The coupling parameters of a quantum field theory can flow even if the corresponding classical field theory is scale-invariant. In this case, the non-zero beta function tells us that the classical scale-invariance is anomalous .
If a beta-function is positive, the corresponding coupling increases with increasing energy. An example is quantum electrodynamics (QED), where one finds by using perturbation theory that the beta-function is positive. In particular, at low energies, α ≈ 1/137, whereas at the scale of the Z boson, about 90 GeV, one measures α ≈ 1/127.
Moreover, the perturbative beta-function tells us that the coupling continues to increase, and QED becomes strongly coupled at high energy. In fact the coupling apparently becomes infinite at some finite energy. This phenomenon was first noted by Lev Landau, and is called the Landau pole. However, one cannot expect the perturbative beta-function to give accurate results at strong coupling, and so it is likely that the Landau pole is an artefact of applying perturbation theory in a situation where it is no longer valid. The true scaling behaviour of at large energies is not known.
In non-Abelian gauge theories, the beta function can be negative, as first found by Frank Wilczek, David Politzer and David Gross. An example of this is the beta-function for Quantum Chromodynamics (QCD), and as a result the QCD coupling decreases at high energies.
Furthermore, the coupling decreases logarithmically, a phenomenon known as asymptotic freedom. The coupling decreases approximately as
Conversely, the coupling increases with decreasing energy. This means that the coupling becomes large at low energies, and one can no longer rely on perturbation theory.
The proton-to-electron mass ratio is primarily determined by the QCD scale.
A boroxol ring doped zigzag boron nitride nanotube: a computational DFT study of the quadrupole coupling constant.(Density functional theory )
Jun 01, 2009; 1. Introduction Various nanostructures of boron nitride (BN) and carbon (C) have been synthesized and studied [1-7]. Much work...
Research Reports from Swiss Federal Institute of Technology Provide New Insights into Chemical Theory and Computation
Nov 23, 2012; By a News Reporter-Staff News Editor at Energy Weekly News -- Fresh data on Chemical Theory and Computation are presented in a...