nLab angular momentum

Idea

In classical mechanics, the analog of momentum for rotational dynamics is called angular momentum, and is defined as twice the product of the mass and the areal velocity.

In quantum mechanics, the angular momentum quantum observables constitute a representation of the (special) orthogonal group $SO(n)$ of $n$-dimensional Euclidean space, in applications typically considered for $n = 3$ or $n = 2$.

Therefore the theory of quantum angular momentum is that of the irreducible representation of the rotation group.

Related concepts

• angular velocity, moment of inertia

• areal velocity

• Clebsch-Gordan coefficient

• spin

• helicity

• Pauli-Lubanski vector

• spin-orbit coupling

• moment map

References

Classical angular momentum

Representation theory of the special orthogonal group

• Wheeler, Irreducible representation of the rotation group (pdf)