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

TL;DR

This paper develops a diagrammatic approach using Schwinger Bosons to analyze non-intersecting electric flux loops in 2+1 dimensional SU(2) lattice gauge theory, enabling a complete characterization of loop dynamics.

Contribution

It introduces a novel diagrammatic technique and fusion variable framework to describe the full non-intersecting loop dynamics in SU(2) lattice gauge theory.

Findings

Physical loop space contains only non-intersecting loops after constraints.

Loop configurations can be generated from basic plaquette loops using fusion operators.

Full Hamiltonian dynamics are expressed in terms of fusion variables.

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.