Editing Canonical coordinates (section)

{{Short description|Sets of coordinates on phase space which can be used to describe a physical system}}
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{{Classical mechanics}}
In [[mathematics]] and [[classical mechanics]], '''canonical coordinates''' are sets of [[coordinates]] on [[phase space]] which can be used to describe a physical system at any given point in time. Canonical coordinates are used in the [[Hamiltonian mechanics|Hamiltonian formulation]] of [[classical mechanics]]. A closely related concept also appears in [[quantum mechanics]]; see the [[Stone–von Neumann theorem]] and [[canonical commutation relation]]s for details.

As Hamiltonian mechanics are generalized by [[symplectic geometry]] and [[canonical transformation]]s are generalized by [[contact transformation]]s, so the 19th century definition of canonical coordinates in classical mechanics may be generalized to a more abstract 20th century definition of coordinates on the [[cotangent bundle]] of a [[manifold]] (the mathematical notion of phase space).