Stratified structure of the observable algebra of Hamiltonian lattice gauge theory

TL;DR

This paper develops a framework to incorporate the stratified classical phase space structure into the quantum observable algebra of Hamiltonian lattice gauge theories, with applications to Yang-Mills theory.

Contribution

It introduces a method to implement classical stratification into the quantum observable algebra using the T-procedure, linking classical orbit types to quantum structures.

Findings

Successfully models classical stratification at the quantum level

Connects classical gauge orbit types with quantum observable algebra

Provides a foundation for analyzing stratified gauge theories

Abstract

We consider Kaehler quantized models whose underlying classical phase space has a stratified structure induced from the Hamiltonian action of a compact Lie group. We show how to implement the classical stratification on the level of the C*-algebra of observables and discuss the relation to the costratification (in the sense of Huebschmann) of the physical Hilbert space. Our analysis is based on the T-procedure as developed by Grundling and Hurst. We apply the general theory to Yang-Mills theory on a finite lattice, where the stratification is given by the classical gauge orbit types.