2004/01/19 by Wolfgang Bertram, Bertram, Wolfgang, Karl‐Hermann Neeb +2
Computer Science · Mathematics · Physics and Astronomy · #17C30 #17C36 #17C65 #17C90 #46H70 #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum optics and atomic interactions #math.DG #math.GR #msc:17C30 #msc:17C36 #msc:17C65 #msc:17C90 #msc:46H70
paper · pdf · doi:10.48550/arxiv.math/0401236
arxiv created 2004/01/19 · openalex publication_date 2004/01/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields \K, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems. This class of spaces, called smooth generalized projective geometries, generalizes the well-known (finite or infinite-dimensional) bounded symmetric domains as well as their ``compact-like'' duals. An interpretation of such geometries as models of Quantum Mechanics is proposed, and particular attention is paid to geometries that might be considered as "standard models" -- they are associated to associative continuous inverse algebras and to Jordan algebras of hermitian elements in such an algebra.