Geodesic
Phase space curvature
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, 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. 
M. G. Ivanov. Phase space curvature. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 130 (2013) no. 1, pp. 361-368. http://geodesic.mathdoc.fr/item/VSGTU_2013_130_1_a36/
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[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.