Non-analytic mass behaviour and the renormalization group

Abstract

In 't Hooft-Weinberg renormalized spinor quantum electrodynamics, the leading mass singularity for m → 0 is found to be m 3(−ln m) 10 for gauge-invariant vertex functions at non-exceptional momentum configurations, and m 2(− ln m) 7 2 for gauge-dependent vertex functions, where m is the renormalized mass parameter. The corresponding result inside the Gell-Mann-Low renormalization scheme, where the renormalized mass parameter is the physical electron mass m phys, is m phys(− ln m phys ) −9 4 in both cases. Analogous results can be found in an asymptotically free non-Abelian gauge theory, provided an infrared-stable fixed-point in coupling-constant space is present. The results are obtained by means of a renormalization group method developed by Symanzik.