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Topological obstructions to the existence of a quantum conservation laws. (English. Russian original) Zbl 1072.81015
Dokl. Math. 71, No. 2, 300-302 (2005); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 401, No. 5, 603-606 (2005).
The existence of non-trivial polynomial differential Hamilton operators for a multidimensional quantum system is considered an. Estimations of the number of independent differential operators, which commute with the Hamilton operator, is performed on the base of reduction to geodetic equations. This number does not exceed the Birkhoff number (homogeneous polynomials of momenta), which in turn depends on topological characteristics of the manifold.

81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
37J05 Relations of dynamical systems with symplectic geometry and topology (MSC2010)