In physics, the canonical commutation relation is the relation
among the position x and momentum p of a point particle in one dimension, where [x,p] = xp - px is the so-called commutator of x and p, i is the imaginary unit and is the reduced Planck's constant. This relation is attributed to Heisenberg, and it implies his uncertainty principle.
In mathematics and physics, the canonicalcoordinates are a special set of coordinates on the cotangent bundle of a manifold.
A change of coordinates that preserves this form is a canonical transformation; these are a special case of a symplectomorphism, which are essentially a change of coordinates on a symplectic manifold.
When a Hamiltonian is defined on the cotangent bundle, then the generalized coordinates are related to the canonicalcoordinates by means of the Hamilton-Jacobi equations.