Proceedings of the International Conference on Geometry, Integrability and Quantization

On Uncertainty, Braiding and Jacobi Fields in Geometric Quantum Mechanics

Alberto Benvegnù

Abstract

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.

Article information

Source
Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Manuel de León, eds. (Sofia: Softex, 2007), 127-137

Dates
First available in Project Euclid: 13 July 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1436792823

Digital Object Identifier
doi:10.7546/giq-8-2007-127-134

Mathematical Reviews number (MathSciNet)
MR2341198

Zentralblatt MATH identifier
1138.81312

Citation

Benvegnù, Alberto. On Uncertainty, Braiding and Jacobi Fields in Geometric Quantum Mechanics. Proceedings of the Eighth International Conference on Geometry, Integrability and Quantization, 127--137, Softex, Sofia, Bulgaria, 2007. doi:10.7546/giq-8-2007-127-134. https://projecteuclid.org/euclid.pgiq/1436792823


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