Exact asymptotic form for the β function in quantum electrodynamics

Abstract

It is shown that the asymptotic form of the Gell-Mann-Low function in quantum electrodynamics can be determined exactly: β(g) = g for g → ∞, where g = e 2 is the running fine-structure constant. This solves the problem of electrodynamics at small distances L (for which dependence g ∞ L −2 holds) and completely eliminates the problem of “zero charge.”