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We construct canonical transformations to reformulate SU(N) Kogut-Susskindlattice gauge theory in terms of a set of fundamental loop & string fluxoperators 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 offreedom become cyclic and decouple from the physical Hilbert space ${\calH}^p$. The canonical relations between the initial SU(N) link operators and thefinal SU(N) loop & string operators over the entire lattice are worked out in aself consistent manner. The Kogut-Susskind Hamiltonian rewritten in terms ofthe fundamental physical loop operators has global SU(N) invariance. There areno gauge fields. We further show that the $(1/g^2)$ magnetic field terms onplaquettes create and annihilate the fundamental plaquette loop fluxes whilethe $(g^2)$ electric field terms describe all their interactions. In the weakcoupling ($g^2 \rightarrow 0$) continuum limit the SU(N) loop dynamics isdescribed by SU(N) spin Hamiltonian with nearest neighbour interactions. In thesimplest SU(2) case, where the canonical transformations map the SU(2) loopHilbert space into the Hilbert spaces of hydrogen atoms, we analyze the specialrole of the hydrogen atom dynamical symmetry group $SO(4,2)$ in the loopdynamics and the spectrum. A simple tensor network ansatz in the SU(2) gaugeinvariant hydrogen atom loop basis is discussed.

Canonical Transformations and Loop Formulation of SU(N) Lattice Gauge Theories