Finite-group gauge theories on lattices as Hamiltonian systems with constraints

TL;DR

This paper explores finite-group lattice gauge theories as Hamiltonian systems with constraints, providing a geometric perspective and connecting to quantum computation models like Kitaev's Quantum Double.

Contribution

It offers a novel interpretation of finite-group lattice gauge theories as constrained Hamiltonian systems, bridging classical gauge theories and quantum computational models.

Findings

Interprets lattice gauge theories as Hamiltonian systems with constraints

Provides geometric insights into Kitaev Quantum Double Models

Links gauge theories to quantum computation frameworks

Abstract

In this work, we present a brief but insightful overview of the gauge theories, which are defined on $ n $-dimensional lattices by using finite gauge groups, in order to show how they can be interpreted as a Hamiltonian system with constraints, analogous to what happens with the classical (continuous) gauge (field) theories. As this interpretation is not usually explored in the literature that discusses/introduces the concept of lattice gauge theory, but some recent works have been exploring Hamiltonian models in order to support some kind of quantum computation, we use this interpretation to, for example, present a brief geometric view of one class of these models: the Kitaev Quantum Double Models.