14 - On the Early Days of the Renormalization Group

Summary

In the spring of 1955 in Moscow there was a small conference on QED and elementary particle theory that took place at the Lebedev Physical Institute from March 31 through April 7. Among the participants were a few foreigners, including Ning Hu and Gunnar Källen. I remember it quite well as it was my first conference on quantum field theory (QFT) problems with scientists from abroad. My short contribution concerned finite Dyson transformations for renormalized Green's functions and matrix elements in QED.

The central point of the conference was Lev Davydovich Landau's review talk “Basic Problems of Quantum Field Theory,” devoted to the ultraviolet behavior in local QFT. The point is that a few months earlier, the problem of short-distance behavior in QED was successfully attacked by Landau and his brilliant pupils Alesha Abrikosov and Isaak Khalatnikov. They managed to find a closed approximation to the Schwinger–Dyson equations for two propagators and the three-vertex function that was compatible with renormalizability and gauge invariance. Besides, this so-called three-gammas approximation admitted a solution in the massless limit that, in modern terms, was equivalent to the summation of leading ultraviolet logarithms.

This solution had a peculiar feature that was controversial from the physical point of view (the “ghost-pole” in the renormalized photon propagator amplitude or Moscow-zero puzzle in the formal expression for the “physical electron charge”) that attracted attention and excited one's imagination.