Geodesic
Phase space curvature
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 361-368.

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Electromagnetic field in classical and quantum mechanics is naturally represented by geometry of extended phase space, with extra coordinates of time and canonically conjugate momentum $p_0=-E$.
Keywords: phase space, quantum mechanics, gauge symmetry, curvature, noncommutative geometry. 
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M. G. Ivanov. Phase space curvature. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 361-368. http://geodesic.mathdoc.fr/item/VSGTU_2013_1_a36/

[1] H. Weyl, The Theory of Groups and Quantum Mechanics, Dover, New York, 1931, 444 pp.; G. Veil, Teoriya grupp i kvantovaya mekhanika, Nauka., M., 1986, 496 pp. | MR

[2] L. D. Faddeev, O. A. Yakubovskii, Lectures on Quantum Mechanics for Mathematics Students, Student Mathematical Library, 47, American Mathematical Society, Providence, RI, 2009, xii+234 pp. | MR | Zbl

[3] J. Bellissard, “Noncommutative Geometry of Aperiodic Solids”, Geometric and Topological Methods for Quantum Field Theory (Villa de Leyva, 2001), World Sci. Publishing, River Edge, NJ, 2003, 86–156 | DOI | MR | Zbl

[4] J. M. Isidro, M. A. de Gosson, “A gauge theory of quantum mechanics”, Mod. Phys. Lett. A., 22:3 (2007), 191–200 | DOI | MR | Zbl

[5] M. G. Ivanov, How to understand quantum mechanics, RKhD, Moscow, Izhevsk, 2012, 516 pp.