The configuration space of low-dimensional Yang-Mills theories

1998/01/26 by T. Pause, T. Heinzl
Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary value problem #Classical mechanics #Computer science #Configuration space #Degrees of freedom (physics and chemistry) #Faddeev–Popov ghost #Gauge (firearms) #Gauge fixing #Gauge theory #Gravitational singularity #Invariant (physics) #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Space (punctuation) #Theoretical physics #Yang–Mills existence and mass gap #Yang–Mills theory #hep-ph #hep-th

paper · pdf · doi:10.1016/s0550-3213(98)00260-0

published as Nucl.Phys. B524 (1998) 695-741 · 52 pages LaTeX2e, 8 postscript figures, uses epsfig, amsmath, amssymb

arxiv created 1998/01/26 · openalex publication_date 1998/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities.

Citations

• Geometry, Topology and Physics
• Quantization of non-Abelian gauge theories
• The Monopole Dominance in QCD
• Generalized Hamiltonian Dynamics
• Yang-Mills fields and Riemannian geometry
• Phase space structure and the path integral for gauge theories on a cylinder
• Quarks, Gluons and Lattices
• Some remarks on the Gribov ambiguity
• Conservation of Isotopic Spin and Isotopic Gauge Invariance