Hidden Symmetries of Dynamics in Classical and Quantum Physics
arXiv:1411.1262 · doi:10.1103/RevModPhys.86.1283
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.
54 pages, review article. To be published in Rev. Mod. Phys
References in corpus (59)
- General Kerr-NUT-AdS Metrics in All Dimensions
- Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
- Non-relativistic conformal symmetries and Newton-Cartan structures
- Complete Integrability of Geodesic Motion in General Kerr-NUT-AdS Spacetimes
- Self-isospectrality, special supersymmetry, and their effect on the band structure
- `Hidden' Symmetries of Higher Dimensional Rotating Black Holes
- Higher-Dimensional Black Holes: Hidden Symmetries and Separation of Variables
- Hidden Symmetry of Higher Dimensional Kerr-NUT-AdS Spacetimes
- The Srni lectures on non-integrable geometries with torsion
- Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity
- Hidden supersymmetry in quantum bosonic systems
- Robinson-Trautman spacetimes in higher dimensions
- Type D Einstein spacetimes in higher dimensions
- Galilean Isometries
- Closed conformal Killing-Yano tensor and Kerr-NUT-de Sitter spacetime uniqueness
- Electromagnetic Properties of Kerr-Anti-de Sitter Black Holes
- Separability of Dirac equation in higher dimensional Kerr-NUT-de Sitter spacetime
- Charged Rotating Black Holes in Odd Dimensions
- Aharonov-Bohm effect on AdS_2 and nonlinear supersymmetry of reflectionless Poschl-Teller system
- On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions
- Constants of Geodesic Motion in Higher-Dimensional Black-Hole Spacetimes
- Generalized hidden symmetries and the Kerr-Sen black hole
- Rotating Einstein-Maxwell-Dilaton Black Holes in D Dimensions
- Covariant hamiltonian dynamics
- Complete Set of Commuting Symmetry Operators for the Klein-Gordon Equation in Generalized Higher-Dimensional Kerr-NUT-(A)dS Spacetimes
- Closed conformal Killing-Yano tensor and geodesic integrability
- Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets
- Hidden nonlinear supersymmetry of finite-gap Lame equation
- Symmetries of the Dirac operator with skew-symmetric torsion
- Higher dimensional rotating black holes in Einstein-Maxwell theory with negative cosmological constant
- Hidden symmetry of hyperbolic monopole motion
- The effective action of the heterotic string compactified on manifolds with SU(3) structure
- Robinson-Trautman spacetimes with an electromagnetic field in higher dimensions
- Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
- Closed conformal Killing-Yano tensor and uniqueness of generalized Kerr-NUT-de Sitter spacetime
- Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
- New Black Holes in Five Dimensions
- Explicit Toric Metric on Resolved Calabi-Yau Cone
- Klein tunneling in carbon nanostructures: a free particle dynamics in disguise
- Kerr-Schild Structure and Harmonic 2-forms on (A)dS-Kerr-NUT Metrics
- Hidden nonlinear su(2|2) superunitary symmetry of N=2 superextended 1D Dirac delta potential problem
- Killing-Yano equations and G-structures
- Kohn's Theorem, Larmor's Equivalence Principle and the Newton-Hooke Group
- Carter-like constants of the motion in Newtonian gravity and electrodynamics
- Hidden symmetry in the presence of fluxes
- Parallel-propagated frame along null geodesics in higher-dimensional black hole spacetimes
- Hidden symmetries of Eisenhart-Duval lift metrics and the Dirac equation with flux
- Resolutions of Cones over Einstein-Sasaki Spaces
- All the timelike supersymmetric solutions of all ungauged d=4 supergravities
- Conserved quantities in non-abelian monopole fields
- Hidden Symmetries of Higher-Dimensional Black Hole Spacetimes
- Non-relativistic scattering of a spin-1/2 particle off a self-dual monopole
- Solving parallel transport equations in the higher-dimensional Kerr-NUT-(A)dS spacetimes
- Charged-rotating black holes and black strings in higher dimensional Einstein-Maxwell theory with a positive cosmological constant
- Geometry of Lax pairs: particle motion and Killing-Yano tensors
- Peculiarities of the hidden nonlinear supersymmetry of Poschl-Teller system in the light of Lame equation
- Dynamal (super)symmetries of monopoles and vortices
- Geometry of the energy landscape and folding transition in a simple model of a protein
- Electron in higher-dimensional weakly charged rotating black hole spacetimes
Cited by in corpus (12)
- The Eisenhart lift: a didactical introduction of modern geometrical concepts from Hamiltonian dynamics
- Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
- Ricci-flat spacetimes admitting higher rank Killing tensors
- Dynamics and exact Bianchi I spacetimes in Einstein-aether scalar field theory
- Principal Tensor Strikes Again: Separability of Vector Equations with Torsion
- Self-dual metrics with maximally superintegrable geodesic flows
- Gauged twistor spinors and symmetry operators
- Hidden Symmetries in Deformed Very Special Relativity
- Complex Lagrangian dynamics
- Hidden symmetries of black holes in five-dimensional supergravity
- Hidden symmetries and nonlinear (super)algebras
- Rigidity of Killing-Yano and conformal Killing-Yano superalgebras