1995/12/19 by William Arveson, Arveson, William · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9512003
39 pages, AMS-TeX
arxiv created 1995/12/19 · openalex publication_date 1995/12/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a noncommutative dynamical system of the type that occurs in quantum theory can often be associated with a dynamical principle; that is, an infinitesimal structure that completely determines the dynamics. The nature of these dynamical principles is similar to that of the second order differential equations of classical mechanics, in that one can locate a space of momentum operators, a ``Riemannian metric", and a potential. These structures are classified in terms of geometric objects which, in the simplest cases, occur in finite dimensional matrix algebras. As a consequence, we obtain a new classification of E0-semigroups acting on type I factors.