  We solve the Gauss law as well as the corresponding Mandelstam constraints of
(d+1) dimensional SU(2) lattice gauge theory in terms of harmonic oscillator
prepotentials. This enables us to explicitly construct a complete orthonormal
and manifestly gauge invariant basis in the physical Hilbert space. Further, we
show that this gauge invariant description represents networks of unoriented
loops carrying certain non-negative abelian fluxes created by the harmonic
oscillator prepotentials. The loop network is characterized by $3(d-1)$ gauge
invariant integers at every lattice site which is the number of physical
degrees of freedom. Time evolution involves local fluctuations of these loops.
The loop Hamiltonian is derived. The generalization to SU(N) gauge group is
discussed.
