2013/02/21 by Fabrizio Canfora, Patricio Salgado-Rebolledo
Mathematics · Physics and Astronomy · #Ansatz #Black Holes and Theoretical Physics #Boundary value problem #Combinatorics #Computer science #Elliptic function #Generalization #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Network topology #Noncommutative and Quantum Gravity Theories #Physics #Quantum Chromodynamics and Particle Interactions #Topology (electrical circuits) #hep-th
paper · pdf · doi:10.1103/physrevd.87.045023
published as Physical Review D 87, 045023 (2013) · 25 pages; Version accepted for publication on Physical Review D. New References included
openalex publication_date 2013/02/21 · arxiv created 2013/04/05 · arxiv updated 2015/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with nontrivial topologies but flat metric, (such as closed tubes S1\ifmmode×\else\texttimes\fiD2, or ℝ\ifmmode×\else\texttimes\fiT2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with nontrivial topologies.