In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p) → (Q, P) that preserves the form of Hamilton's equations...

theorem and canonical commutation relations for details. As Hamiltonian mechanics are generalized by symplectic geometry and canonical transformations are generalized...

In Hamiltonian mechanics, the linear canonical transformation (LCT) is a family of integral transforms that generalizes many classical transforms. It has...

coordinate transformations, called canonical transformations, which map canonical coordinate systems into canonical coordinate systems. A "canonical coordinate...

that they become Fourier transform duals Canonical transformation, in Hamiltonian mechanics Grand canonical ensemble, a probability distribution of microscopic...

which acts as a bridge between two sets of canonical variables when performing a canonical transformation. There are four basic generating functions,...

homogeneous system. The Bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra...

tightened in the linear canonical transformation, discussed below. From the point of view of the linear canonical transformation, Fresnel diffraction can...

treating S {\displaystyle S} as the generating function for a canonical transformation of the classical Hamiltonian H = H ( q 1 , q 2 , … , q N ; p 1...

published, based upon a stationary phase approximation. Linear canonical transformations are the linear transforms of the time–frequency representation...