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Traditionally, fundamental theories of nature have had a tendency to break down at short distances. This often signals the appearance of new physics that is discovered once one has experimental instruments of high enough resolution to explore the higher energy regime. Before asymptotic freedom it was expected that any quantum field theory would fail at sufficiently high energy, where the flaws of the renormalization procedure would appear. To deal with this, one would have to invoke some kind of fundamental length. In an asymptotically free theory this is not necessarily the case — the decrease of the effective coupling for large energy means that no new physics need arise at short distances. There are no infinities at all, the bare coupling is finite — indeed it vanishes. The only divergences that arise are an illusion that appears when one tries to compare, in perturbation theory, the finite effective coupling at finite distances with the vanishing effective coupling at infinitely short distances.
Thus the discovery of asymptotic freedom greatly reassured one of the consistency of four-dimensional quantum field theory. One can trust renormalization theory for an asymptotically free theory, independent of the fact that perturbation theory is only an asymptotic expansion, where it gets better and better in the regime of short distances. (en) |
