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Zbl 1138.81312
Benvegnù, Alberto
On uncertainty, braiding and Jacobi fields in geometric quantum mechanics. (English)
[A] Mladenov, Iva\"ilo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9--14, 2006. Sofia: Bulgarian Academy of Sciences. 127-134 (2007). ISBN 978-954-8495-37-0/pbk

Summary: Acting within the framework of the geometric quantum mechanics, we give a Jacobi field interpretation of the quantum mechanical uncertainty. Then a link with elliptic curves via the classical integrability of Schrödinger dynamics and the cross ratio interpretation of quantum probabilities is established. Furthermore a geometrical construction of all special unitary representations of the three-strand braid group on the quantum one-qubit space is provided.

MSC 2000:: *81P05 General and philosophical topics in quantum theory
51N15 Projective analytic geometry
81P99 Axiomatics, foundations, philosophy of quantum theory

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