On uncertainty, braiding and Jacobi fields in geometric quantum mechanics. (English) Zbl 1138.81312

Mladenov, Ivaïlo (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 (ISBN 978-954-8495-37-0/pbk). 127-134 (2007).
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.
For the entire collection see [Zbl 1108.53003].


81P05 General and philosophical questions in quantum theory
51N15 Projective analytic geometry
81P99 Foundations, quantum information and its processing, quantum axioms, and philosophy