Stratified structure of the observable algebra of Hamiltonian lattice gauge theory
arXiv:1909.10921
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.
Added new section on motivation and background, corrected and revised argument in sections 3.2 and 4.2 (revised version), added comments on the definition of stratified C*-algebra and on the role of the algebra R in section 4.2 (revised version). arXiv admin note: text overlap with arXiv:1803.11077, arXiv:1702.01047