  We construct canonical transformations to reformulate SU(N) Kogut-Susskind
lattice gauge theory in terms of a set of fundamental loop & string flux
operators along with their canonically conjugate loop & string electric fields.
We show that as a consequence of SU(N) Gauss laws all SU(N) string degrees of
freedom become cyclic and decouple from the physical Hilbert space ${\cal
H}^p$. The canonical relations between the initial SU(N) link operators and the
final SU(N) loop & string operators over the entire lattice are worked out in a
self consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms of
the fundamental physical loop operators has global SU(N) invariance. There are
no gauge fields. We further show that the $(1/g^2)$ magnetic field terms on
plaquettes create and annihilate the fundamental plaquette loop fluxes while
the $(g^2)$ electric field terms describe all their interactions. In the weak
coupling ($g^2 \rightarrow 0$) continuum limit the SU(N) loop dynamics is
described by SU(N) spin Hamiltonian with nearest neighbour interactions. In the
simplest SU(2) case, where the canonical transformations map the SU(2) loop
Hilbert space into the Hilbert spaces of hydrogen atoms, we analyze the special
role of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loop
dynamics and the spectrum. A simple tensor network ansatz in the SU(2) gauge
invariant hydrogen atom loop basis is discussed.
