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

Abstract

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.

Appendix added in new version, Accepted for publication in Phys. Rev D. (37 pages, 20 figures)

References in corpus (4)

• Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
• Lattice Gauge Tensor Networks
• Loop Approach to Lattice Gauge Theories
• Irreducible SU(3) Schwinger Bosons

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