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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 ...
Infinitesimal RG transformations map actions to nearby ones, thus giving rise to a vector field on theory space. The scale dependence of an action is encoded in a "running" of the coupling constants parametrizing this action, {} {()}, with the RG scale . This gives rise to a trajectory in theory space (RG trajectory), describing the evolution ...
One example of such a coupling constant is the electric charge. In approximate calculations in several quantum field theories, notably quantum electrodynamics and theories of the Higgs particle , the running coupling appears to become infinite at a finite momentum scale.
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.
In a theory intended to represent a physical interaction where the coupling constant is known to be non-zero, Landau poles or triviality may be viewed as a sign of incompleteness in the theory. For example, QED is usually not believed [ citation needed ] to be a complete theory on its own, because it does not describe other fundamental ...
This series diverges asymptotically, but in quantum electrodynamics (QED) at the second order the difference from experimental data is in the order of 10 −10. This close agreement holds because the coupling constant (also known as the fine-structure constant ) of QED is much less than 1.