1997/10/03 by V. Aldaya, Aldaya, V., Julio Guerrero +4
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.physics/9710002
52 pages, latex, no figures. Contribution to "Symmetries in Science X", held in Bregenz (Austria), 13-18 July 1997. To appear in the proceedings
arxiv created 1997/10/03 · openalex publication_date 1997/10/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Contents * Introduction -- Why S1-extended phase space? -- Why central extensions of classical symmetries? * Central extension \Gt of a group G -- Group cohomology -- Cohomology and contractions: Pseudo-cohomology -- Principal bundle with connection (\Gtm,Θ) * Group Approach to Quantization -- U(1)-quantization -- Non-horizontal polarizations * Simple examples -- The abelian group Rk -- The semisimple group SU(2) * Algebraic anomalies -- Higher-order polarizations -- The Schrödinger group and Quantum Optics -- The Virasoro group and String Theory