On the stratified classical configuration space of lattice QCD (Q2567114)

The stratified structure of the configuration space \(G^N=G \times\cdots\times G\) reduced with respect to the action of \(G\) by inner automorphisms is investigated for \(G=\text{SU}(3)\). 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.