nLab spin

Idea

The spin of a particle in quantum mechanics/quantum field theory is its intrinsic angular momentum, but subject to the possibility that the particle may be a fermion so that that its angular momentum is not determined by the representation theory of the special orthogonal group, but of the spin group.

Properties

Spin-Statistics theorem

By the spin-statistics theorem, the spin of any elementary particle must be (in magnitude) half of an integer multiple of Planck's constant ($\hbar = h/2\pi$), an integer if the particle is a boson but only a half-integer if the particle is a fermion.

Related concepts

• spin group,

• spin representation, real spin representation

• Fierz identity

• proton spin crisis

• spinor

• Dirac spinor, Weyl spinor, Majorana spinor

• Dirac field

• Ising model, Heisenberg model

• quantization of the 2-sphere

• supersymmetry

• division algebras and supersymmetry

• geometry of physics – supersymmetry