Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University3472410.14498/vsgtu1198Research ArticlePhase space curvatureIvanovMikhail GennadievichCandidate of physico-mathematical sciences, Associate professorivanov.mg@mipt.ruMoscow Institute of Physics and Technology (State University)1512201317136136810062020Copyright © 2013, Samara State Technical University2013Electromagnetic field in classical and quantum mechanics is naturally representedby geometry of extended phase space, with extra coordinates of time and canonically conjugate momentum$p_0=-E$.phase spacequantum mechanicsgauge symmetrycurvaturenoncommutative geometryфазовое пространствоквантовая механикакалибровочная симметриякривизнанекоммутативная геометрия[H. Weyl, The Theory of Groups and Quantum Mechanics, Dover, New York, 1931, 444 pp.][Л. Д. Фаддеев, О. А. Якубовский, Лекции по квантовой механике для студентов-математиков, РХД, М., Ижевск, 2001, 256 с.][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][J. M. Isidro, M. A. de Gosson, "A gauge theory of quantum mechanics", Mod. Phys. Lett. A., 22:3 (2007), 191-200][М. Г. Иванов, Как понимать квантовую механику, РХД, М., Ижевск, 2012, 516 с.]