Unique Trajectory Method in Migdal Renormalization Group Approach and SU(2) Lattice Gauge Theory

Abstract

In a preceding paper (Ref. 1)), we presented unique trajectory and applied it to the lattice gauge theory (LGT)2) of the icosahedral subgroup [(120)3) of 5U(2). The unique trajectory method, which is a combined method of Migdal renormalization group approach )-6) and Wilson-Kogut topological argument,7) leads to the relation between the bare coupling constants and the lattice constant by fixing the renormalized coupling constant at some value. The obtained results are interesting because we observed not only the ordinary second order phase transition but also the delicate phenomena like the crossover structureS) and the stepwise transition like a first order phase transition is observed_ These observations suggest that it is valuable to investigate the phase structure of other LGT's like 5U(2), 5U(3), etc. by this method. In this paper, we apply the unique trajectory method to the continuous group 5U(2) case and investigate the detailed p!lase structure. The unique trajectory method is briefly summarized as follows. By the Migdal renormalization group transformation, we obtain trajectories in the space of renormalized coupling constants for various bare theories. All of these trajectories starting from different bare coupling constants converge to a single trajectory by the successive transformations. This is a unique trajectory or a unique renormalized trajectory.7) The existence of this unique trajectory suggests that we can derive a relation between various bare theories with a different bare coupling constant /:Jb and a different lattice constant a by fixing the renormalized coupling constant. Namely, we fix a renormalized coupling constant /:Jc at any point on the unique trajectory, which we call gate, and calculate the