a Re-Examination of the Migdal-Kadanoff Renormalization Group Equations and Construction of the First Order Martinelli - Correction for Lattice Gauge Theories

This dissertation discusses the results of a new technique for determining the Gell-Mann-Low function in lattice gauge theories using Migdal-Kadanoff type recurrence relations. By calculating the scaling parameter for a class of SU(2) lattice actions in the region g('2) (DBLTURN) 0.1 a clear violation of the assumed universality of the continuum limit is demonstrated. This violation is reconciled with earlier calculations using the same recurrence relations by analyzing corrections to approximations involved in them. In addition, I show how to construct the first term in a scheme of systematic corrections proposed by Martinelli and Parisi for d-dimensional SU(N) gauge theories. The form of the correction for SU(2) theories with a Wilson action is derived and evaluated in a simple case. It does not seem likely that such a correction will remove the non-universality.