Keyboard graph navigation: press N for concepts or E for relations; use arrow keys, Home, and End to move; Enter selects; Shift plus Enter selects and centers; plus and minus zoom; zero fits; Escape clears the selection. Use the visible viewport buttons as alternatives to dragging, wheel, and pinch gestures.
Canonical static concept record
Open this concept in the interactive graphRead the Markdown equivalent
A smooth manifold with a closed nondegenerate differential 2-form.
wp-symplectic-manifoldnlab-symplecticlee-smooth-manifoldsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The fundamental form of a Kähler manifold is symplectic.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
wp-kahler-manifoldnlab-kahler-manifoldnlab-symplecticlee-smooth-manifoldsThis is an authored directed relation from the source endpoint to the target endpoint.
Add a differential 2-form that is closed and nondegenerate.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
nlab-symplecticlee-smooth-manifoldsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Supplying a smooth function on a symplectic manifold determines the Hamiltonian vector field by up to the declared sign convention, and hence a local Hamiltonian evolution; global evolution additionally requires completeness.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
wp-symplectic-manifoldwp-math-hamiltonian-systemcambridge-classical-dynamicsThis is an authored directed relation from the source endpoint to the target endpoint.
Hamiltonian mechanics is naturally formulated on symplectic manifolds, whose symplectic form defines Hamiltonian vector fields and Poisson brackets.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
cern-qft-introwp-physics-hamiltonian_mechanicsnlab-physics-hamiltonian_mechanicsnlab-symplecticlee-smooth-manifoldsThis is an authored directed relation from the source endpoint to the target endpoint.
Hamiltonian phase spaces are symplectic manifolds or appropriate generalizations.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-physics-phase_spacenlab-physics-phase_spacenlab-symplecticlee-smooth-manifoldsThis is an authored directed relation from the source endpoint to the target endpoint.
The inverse bivector of a symplectic form defines a Poisson bracket.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
nlab-symplecticwp-poissonlee-smooth-manifolds