2014/01/29 by Marco Benini, Benini, Marco
Mathematics · Physics and Astronomy · #14F40 #81T13 #81T20 #Black Holes and Theoretical Physics #Cohomology #Computer science #De Rham cohomology #Duality (order theory) #Equivariant cohomology #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Mathematical analysis #Mathematics #Observable #Physics #Poincaré duality #Pure mathematics #Quantum mechanics #Space (punctuation) #gr-qc #hep-th #math-ph #math.MP #msc:14F40 #msc:81T13 #msc:81T20
paper · pdf · doi:10.48550/arxiv.1401.7563
26 pages
arxiv created 2014/01/29 · openalex publication_date 2014/01/29 · arxiv updated 2014/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincaré duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincaré duality for the new cohomology groups.