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The dependence of a coupling g(μ) on the energy-scale is known as "running of the coupling". 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 ...
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 ...
The value of the fine-structure constant α is linked to the observed value of this coupling associated with the energy scale of the electron mass: the electron's mass gives a lower bound for this energy scale, because it (and the positron) is the lightest charged object whose quantum loops can contribute to the running.
For quantum chromodynamics, the constant changes with respect to the distance between the particles. This phenomenon is known as asymptotic freedom. Forces which have a coupling constant greater than 1 are said to be "strongly coupled" while those with constants less than 1 are said to be "weakly coupled." [7]
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. [1] [2] [3] In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. [2]
The coupling constant in QED is the fine-structure constant α ≈ 1/137, which is small enough that only the simplest, lowest order, Feynman diagrams need to be considered in realistic calculations. In contrast, the coupling constant in the strong interaction is roughly of the order of one, making complicated, higher order, Feynman diagrams ...
The model belongs to the Griffiths-Simon class, [1] meaning that it can be represented also as the weak limit of an Ising model on a certain type of graph. The triviality of both the ϕ 4 {\displaystyle \phi ^{4}} model and the Ising model in d ≥ 4 {\displaystyle d\geq 4} can be shown via a graphical representation known as the random current ...
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 ...