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.
Canonical quantization of a field theory is analogous to the construction of quantum mechanics from classical mechanics.
The classical field is treated as a dynamical variable called the canonical coordinate, and its time-derivative is the canonicalmomentum.
However, it leads to a fairly simple picture of the vacuum state and is not easily amenable to use in a quantum field theory (such as quantum chromodynamics) which is known to have a complicated vacuum characterized by many different condensates.
In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point.
The reason angular momentum is important in physics is that it is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it.
Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance (As a result, angular momentum isn't conserved for general curved spacetimes, unless it happens to be asymptotically rotationally invariant).
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