Wilson loops in the light of spin networks

TL;DR

This paper demonstrates that Wilson loops form a dense subalgebra of continuous observables in lattice gauge theory for groups composed of orthogonal, unitary, and symplectic factors, providing insight into the structure of gauge theories.

Contribution

It establishes the density of Wilson loops in the algebra of observables for a broad class of structure groups, extending understanding of gauge invariants in lattice theories.

Findings

Wilson loops generate a dense subalgebra of observables

Applicable to groups formed by orthogonal, unitary, and symplectic factors

Enhances understanding of gauge invariants in lattice gauge theory

Abstract

When G is a product of orthogonal, unitary and symplectic groups, we show that the Wilson loops generate a dense subalgebra of continuous observables on the configuration space of lattice gauge theory with structure group G.