1993/06/28 by Shogo Tanimura, Tanimura, Shogo · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Noncommutative and Quantum Gravity Theories #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9306144
34 pages
arxiv created 1993/06/28 · openalex publication_date 1993/06/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A definition of quantum mechanics on a manifold M is proposed and a method to realize the definition is presented. This scheme is applicable to a homogeneous space M = G / H . The realization is a unitary representation of the transformation group G on the space of vector bundle-valued functions. When H ≠ \ e \ , there exist a number of inequivalent realizations. As examples, quantum mechanics on a sphere Sn , a torus Tn and a projective space \RP are studied. In any case, it is shown that there are an infinite number of inequivalent realizations.