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SU(2) Lattice Gauge Theory- Local Dynamics on Non-intersecting Electric flux Loops

We use Schwinger Bosons as prepotentials for lattice gauge theory to define local linking oper- ators and calculate their action on linking states for 2 + 1 dimensional SU(2) lattice gauge theory. We develop a diagrammatic technique and associate a set of (lattice Feynman) rules to compute the entire loop dynamics diagrammatically. The physical loop space is shown to contain only non- intersecting loop configurations after solving the Mandelstam constraint. The smallest plaquette loops are contained in the physical loop space and other configurations are generated by the action of a set of fusion operators on this basic loop states enabling one to charaterize any arbitrary loop by the basic plaquette together with the fusion variables. Consequently, the full Kogut-Susskind Hamiltonian and the dynamics of all possible non-intersecting physical loops are formulated in terms of these fusion variables.