The groupoidal picture of quantum mechanics. (English) Zbl 1540.81072
The purpose of this paper is to give a groupoid interpretation of quantum mechanics. The authors consider a groupoid as the basic mathematical ingredient in the description of a physical system. First, the authors review the relevant notions of the theory of measure groupoids and their link with quantum mechanical systems. Then, they give a construction of the von Neumann algebra of a measure groupoid. The quantum-to-classical transition is interpreted in the groupoid framework. Feynman’s sum over histories interpretation is also described in terms of groupoids.
Reviewer: Angela Gammella-Mathieu (Metz)
MSC:
| 81R15 | Operator algebra methods applied to problems in quantum theory |
| 85A04 | General questions in astronomy and astrophysics |
| 18B40 | Groupoids, semigroupoids, semigroups, groups (viewed as categories) |
| 46L10 | General theory of von Neumann algebras |
| 81Q20 | Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory |
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