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In QED, the $\beta$-function has a positive sign. This means that the coupling increases at higher energies, or equivalently, smaller length scales. This picture is made intuitively clear by the following heuristic argument:

Consider the electron-positron loops in the photon propagator. These fluctuations screen charge in a vacuum, lowering the effective charge. As you move in closer, the charge is less screened, so the coupling should increase.

However, the opposite effect is true for an asymptotically free theory, such as QCD: The beta function is negative. As the length scale decreases, the coupling decreases How should one intuitively interpret asymptotic freedom? Is there a nice argument like the charge-screening picture for QED?

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  • $\begingroup$ The discovery of asymptotic freedom came as a big surprise to Gross, Wilczek, and Politzer, so if there is an intuitive explanation for it it is only obvious in hindsight. $\endgroup$ – G. Smith Oct 16 at 21:25
  • $\begingroup$ Related. Just as in QED, fermions screen color charge; unlike QED, gluons self-couple, and anti-screen, weakening the effective charge with decreasing distance. There are dozens of fairy-tale rationalizations for this, none of them compelling and ineluctable. $\endgroup$ – Cosmas Zachos Oct 16 at 21:53
  • $\begingroup$ Might look at this cartoon, but unless you calculate something meaningful, any "insight" cannot help being illusory. $\endgroup$ – Cosmas Zachos Oct 16 at 22:02

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