On the stratified classical configuration space of lattice QCD

2004/09/29 by S. Charzyński, Szymon Charzyński, J. Kijowski +5
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Automorphism #Black Holes and Theoretical Physics #Configuration space #Geometry #Lattice (music) #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Stratification (seeds) #hep-th

paper · pdf · doi:10.1016/j.geomphys.2004.12.002

published as J.Geom.Phys. 55 (2005) 137-178 · 42 pages, 1 figure

arxiv created 2004/09/29 · openalex publication_date 2005/01/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The stratified structure of the configuration space \mb G^N = G × ... × 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.

Citations

• Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics
• Smooth functions invariant under the action of a compact lie group
• The invariant theory of n × n matrices
• Stratified Symplectic Spaces and Reduction