Abstract
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analysed from this perspective, the relevant geometrical structures and their associated algebraic properties are highlighted, and the Qubit example is thoroughly discussed.
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Notes
- 1.
\(\mathscr {H}_{0}\) denotes the Hilbert space \(\mathscr {H}\) with the zero vector removed.
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Acknowledgements
The authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in RD (SEV-2015/0554). AI would like to thank partial support provided by the MINECO research project MTM2017-84098-P and QUITEMAD+, S2013/ICE-2801. GM would like to thank the support provided by the Santander/UC3M Excellence Chair Programme.
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Ciaglia, F.M., Ibort, A., Marmo, G. (2019). Differential Geometry of Quantum States, Observables and Evolution. In: Ballico, E., Bernardi, A., Carusotto, I., Mazzucchi, S., Moretti, V. (eds) Quantum Physics and Geometry. Lecture Notes of the Unione Matematica Italiana, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-06122-7_7
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