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Hence, the actual value of the coupling constant is only defined at a given energy scale. In QCD, the Z boson mass scale is typically chosen, providing a value of the strong coupling constant of α s (M Z 2) = 0.1179 ± 0.0010. [7] In 2023 Atlas measured α s (M Z 2) = 0.1183 ± 0.0009 the most precise so far.
Richard Feynman, one of the originators and early developers of the theory of quantum electrodynamics (QED), referred to the fine-structure constant in these terms: There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a ...
written in terms of the fine structure constant in natural units, α = e 2 /4π. [2] This beta function tells us that the coupling increases with increasing energy scale, and QED becomes strongly coupled at high energy. In fact, the coupling apparently becomes infinite at some finite energy, resulting in a Landau pole. However, one cannot ...
Because the theory is "sick" for any negative value of the coupling constant, the series does not converge but is at best an asymptotic series. From a modern perspective, we say that QED is not well defined as a quantum field theory to arbitrarily high energy. [30] The coupling constant runs to infinity at finite energy, signalling a Landau pole.
The scale anomaly, which gives rise to a running coupling constant. In QED this gives rise to the phenomenon of the Landau pole. In quantum chromodynamics (QCD) this leads to asymptotic freedom. The chiral anomaly in either chiral or vector field theories with fermions. This has close connection with topology through the notion of instantons.
The renormalization group prediction (cf. Stueckelberg–Petermann and Gell-Mann–Low works) was confirmed 40 years later at the LEP accelerator experiments: the fine structure "constant" of QED was measured [6] to be about 1 ⁄ 127 at energies close to 200 GeV, as opposed to the standard low-energy physics value of 1 ⁄ 137.
The problem of the Landau pole in QED is of purely academic interest, for the following reason. The role of g obs in Eqs. 1, 2 is played by the fine structure constant α ≈ 1/137 and the Landau scale for QED is estimated as 10 286 eV, which is far beyond any energy scale relevant to
In classical field theory, such as gauge theory in four-dimensional spacetime, the coupling constant is a dimensionless constant. However, upon quantization, logarithmic divergences in one-loop diagrams of perturbation theory imply that this "constant" actually depends on the typical energy scale of the processes under considerations, called ...