1999/08/18 by P. Hájı́ček, P. Hajicek, Jerzy Kijowski +1 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Cosmology and Gravitation Theories #Covariant transformation #Decomposition #Gauge (firearms) #Gauge group #Gauge theory #Geography #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Pure mathematics #Quantum Electrodynamics and Casimir Effect #Space (punctuation) #gr-qc
paper · pdf · doi:10.1103/physrevd.61.024037
published as Phys.Rev. D61 (2000) 024037 · Revtex, 35 pages, no figures
arxiv created 1999/08/18 · openalex publication_date 1999/12/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The symplectic geometry of a broad class of generally covariant models is studied. The class is restricted so that the gauge group of the models coincides with the Bergmann-Komar group and the analysis can focus on the general covariance. A geometrical definition of gauge fixing at the constraint manifold is given; it is equivalent to a definition of a background (spacetime) manifold for each topological sector of a model. Every gauge fixing defines a decomposition of the constraint manifold into the physical phase space and the space of embeddings of the Cauchy manifold into the background manifold (Kucha\ifmmode \checkr\else \vr\fi decomposition). Extensions of every gauge fixing and the associated Kucha\ifmmode \checkr\else \vr\fi decomposition to a neighborhood of the constraint manifold are shown to exist.