Hamiltonian lattice gauge models and the Heisenberg double

TL;DR

This paper constructs Hamiltonian lattice gauge models using the Heisenberg double of a Lie group in any dimension, introducing vertex operators for gauge-invariant observables that approach unity in the continuum limit.

Contribution

It presents a novel formulation of lattice gauge models based on the Heisenberg double, extending to arbitrary dimensions and detailing the behavior of Wilson line observables.

Findings

Hamiltonian models are constructed in arbitrary dimensions.

Gauge-invariant Wilson lines require vertex operators.

Vertex operators approach unity in the continuum limit.

Abstract

Hamiltonian lattice gauge models based on the assignment of the Heisenberg double of a Lie group to each link of the lattice are constructed in arbitrary space-time dimensions. It is shown that the corresponding generalization of the gauge-invariant Wilson line observables requires to attach to each vertex of the line a vertex operator which goes to the unity in the continuum limit.