Hidden Symmetries of Dynamics in Classical and Quantum Physics

TL;DR

This paper reviews the significance of hidden symmetries in classical and quantum physics, highlighting their role in conserved quantities, integrability, and applications across diverse physical systems and theories.

Contribution

It provides a comprehensive overview of hidden symmetries, their emergence in various physical contexts, and recent developments in understanding their role in complex dynamical systems.

Findings

Identification of hidden symmetries in diverse systems

Connection between symmetries and integrability

Applications to black holes, supergravity, and quantum equations

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 non-relativistic, 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 non-trivial 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, supergravity with and without fluxes, providing a tool to probe the dynamics of non-linear systems.