We study the Migdal recursion relations and the reformulation due to Kadanoff for SU(2) and SU(3) lattice gauge theory, using analytic approximations for large and small couplings and numerical methods for all couplings. In SU(2) we obtain the beta function and the expectation value of the plaquette, which is compared with recent Monte Carlo results. In analogy to U(1), we find that a Villain form (periodic gaussian) for the exponential of the plaquette action is a good approximation to the result of the Migdal renormalization transformation. We also perform some calculations in SU(3) and find that its behavior is similar to SU(2).
ASJC Scopus subject areas
- Nuclear and High Energy Physics