Editing Symplectomorphism (section)

==Quantizations==
Representations of finite-dimensional subgroups of the group of symplectomorphisms (after ħ-deformations, in general) on [[Hilbert space]]s are called ''quantizations''. 
When the Lie group is the one defined by a Hamiltonian, it is called a "quantization by energy". 
The corresponding operator from the [[Lie algebra]] to the Lie algebra of continuous linear operators is also sometimes called the ''quantization''; this is a more common way of looking at it in physics.

{{see also| phase space formulation| geometric quantization|non-commutative geometry}}