Coupling constant
Originally, the coupling constant related the force acting between two static bodies to the "charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared,This description remains valid in modern physics for linear theories with static bodies and massless force carriers.By looking at the QED Lagrangian, one sees that indeed, the coupling sets the proportionality between the kinetic termFor example, one often sets up hierarchies of approximation based on the importance of various coupling constants.Another important example of the central role played by coupling constants is that they are the expansion parameters for first-principle calculations based on perturbation theory, which is the main method of calculation in many branches of physics.A special role is played in relativistic quantum theories by couplings that are dimensionless; i.e., are pure numbers.This constant is proportional to the square of the coupling strength of the charge of an electron to the electromagnetic field.), like in QED, QCD, and the weak interaction, the theory is renormalizable and all the terms of the expansion series are finite (after renormalization).Perturbation expansions in the coupling might still be feasible, albeit within limitations,[2][3] as most of the higher order terms of the series will be infinite.With a high frequency (i.e., short time) probe, one sees virtual particles taking part in every process.The foregoing remark only applies to some formulations of quantum field theory, in particular, canonical quantization in the interaction picture.The theory of the running of couplings is given by the renormalization group, though it should be kept in mind that the renormalization group is a more general concept describing any sort of scale variation in a physical system (see the full article for details).[4] As explained in the introduction, the coupling constant sets the magnitude of a force which behaves with distance asfrom the body A generating a force, this one is proportional to the field flux going through an elementary surface S perpendicular to the line AB.As the flux spreads uniformly through space, it decreases according to the solid angle sustaining the surface S. In the modern view of quantum field theory, the), more force carriers are involved or particle pairs are created, see Fig.Since the additional particles involved beyond the single force carrier approximation are always virtual, i.e. transient quantum field fluctuations, one understands why the running of a coupling is a genuine quantum and relativistic phenomenon, namely an effect of the high-order Feynman diagrams on the strength of the force.In quantum field theory, a beta function, β(g), encodes the running of a coupling parameter, g. It is defined by the relation where μ is the energy scale of the given physical process.In this case, the non-zero beta function tells us that the classical scale-invariance is anomalous.An example is quantum electrodynamics (QED), where one finds by using perturbation theory that the beta function is positive.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 artifact of applying perturbation theory in a situation where it is no longer valid.[4] Furthermore, the coupling decreases logarithmically, a phenomenon known as asymptotic freedom (the discovery of which was awarded with the Nobel Prize in Physics in 2004).is the energy of the process involved and β0 is a constant first computed by Wilczek, Gross and Politzer.This means that the coupling becomes large at low energies, and one can no longer rely on perturbation theory.In QCD, the Z boson mass scale is typically chosen, providing a value of the strong coupling constant of αs(MZ2 ) = 0.1179 ± 0.0010.[5][6] The most precise measurements stem from lattice QCD calculations, studies of tau-lepton decay, as well as by the reinterpretation of the transverse momentum spectrum of the Z boson.The meaning of the minimal subtraction (MS) scheme scale ΛMS is given in the article on dimensional transmutation.A remarkably different situation exists in string theory since it includes a dilaton.These coupling constants are not pre-determined, adjustable, or universal parameters; they depend on space and time in a way that is determined dynamically.Sources that describe the string coupling as if it were fixed are usually referring to the vacuum expectation value.
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