Hidden symmetries of dynamics in classical and quantum physics

Marco Cariglia
Rev. Mod. Phys. 86, 1283 – Published 22 December 2014

Abstract

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description of physical systems as varied as nonrelativistic, relativistic, with or without gravity, classical or quantum, and are related to the existence of conserved quantities of the dynamics and integrability. In recent years their study has grown intensively, due to the discovery of nontrivial examples that apply to different types of theories and different numbers of dimensions. Applications encompass the study of integrable systems such as spinning tops, the Calogero model, systems described by the Lax equation, the physics of higher-dimensional black holes, the Dirac equation, and supergravity with and without fluxes, providing a tool to probe the dynamics of nonlinear systems.

  • Received 13 March 2014

DOI:https://doi.org/10.1103/RevModPhys.86.1283

© 2014 American Physical Society

Authors & Affiliations

Marco Cariglia*

  • DEFIS, Universidade Federal de Ouro Preto, Campus Morro do Cruzeiro, 35400-000 Ouro Preto, MG—Brasil

  • *marco@iceb.ufop.br

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Issue

Vol. 86, Iss. 4 — October - December 2014

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