  We solve the Gauss law and the corresponding Mandelstam constraints in the
loop Hilbert space ${\cal H}^{L}$ using the prepotential formulation of $(d+1)$
dimensional SU(2) lattice gauge theory. The resulting orthonormal and complete
loop basis, explicitly constructed in terms of the $d(2d-1)$ prepotential
intertwining operators, is used to transcribe the gauge dynamics directly in
${\cal H}^{L}$ without any redundant gauge and loop degrees of freedom. Using
generalized Wigner-Eckart theorem and Biedenharn -Elliot identity in ${\cal
H}^L$, we show that the loop dynamics for pure SU(2) lattice gauge theory in
arbitrary dimension, is given by the real symmetric $3nj$ symbols of first kind
(e.g., n=6, 10 for d=2, 3 respectively). The corresponding "ribbon diagrams"
representing SU(2) loop dynamics are constructed. The prepotential techniques
are trivially extended to include fundamental matter fields leading to a
description in terms of loops and strings. The SU(N) gauge group is briefly
discussed.
