Multiscale Gauge Invariance

The principle of symmetry with respect to local gauge transformations psi(x) -> e(iw(x))psi has been extended to fields psi(g) <chi vertical bar Omega*(g)psi > defined on a locally compact Lie group, g is an element of G, where Omega(g) is a square-integrable representation of. It has been shown that if is an affine group, one G : x' ax + b, x, b, is an element of R-d, one can construct a quantum field model with a gauge group SU(N) that is free of both UV and IR divergences.