On the Algebraic Structure of Globally or Locally SU (2) Invariant Lattice Field Theories

The local contribution to the action of the O (3) σ model in D = 2 or pure SU (2) gauge models in D ≧ 3 dimensions are expanded and integrated on the group. There results a field of variables j , a 3 nj coefficient W ({ j }) with n → ∞ and dynamical factors f ( j , β). We prove that for the gauge models a local decomposition of W ({ j }) into a product of 3 nj coefficients with n = 2 D ( D – 2) exists. We study generating functions for W ({ j }) or the 3 nj coefficients and develop an algorithm for their computation. Some of these generating functions are explicitly calculated.