On the Stratified Classical Configuration Space of Lattice QCD

TL;DR

This paper analyzes the stratified structure of the classical configuration space in lattice QCD for G=SU(3), characterizing invariants and geometric strata for small N, providing a detailed algebraic and geometric understanding.

Contribution

It offers a detailed algebraic and geometric characterization of the stratified configuration space in lattice QCD for small N, including explicit descriptions of strata and invariants.

Findings

Stratification characterized algebraically for arbitrary N.

Full algebra of invariants discussed for N=1 and N=2.

Explicit characterization of strata using local cross sections.

Abstract

The stratified structure of the configuration space $\mb G^N = G \times ... \times G$ reduced with respect to the action of $G$ by inner automorphisms is investigated for $G = SU(3) .$ This is a finite dimensional model coming from lattice QCD. First, the stratification is characterized algebraically, for arbitrary $N$. Next, the full algebra of invariants is discussed for the cases $N = 1$ and $N =2 .$ Finally, for $N = 1$ and $N =2 ,$ the stratified structure is investigated in some detail, both in terms of invariants and relations and in more geometric terms. Moreover, the strata are characterized explicitly using local cross sections.