Spin network

In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics.

[1] Spin networks have since been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin, Rodolfo Gambini and others.

Spin networks can also be used to construct a particular functional on the space of connections which is invariant under local gauge transformations.

A unit with spin number n is called an n-unit and has angular momentum nħ/2, where ħ is the reduced Planck constant.

The formula for area eigenvalues becomes somewhat more complicated if the surface is allowed to pass through the vertices, as with anomalous diffusion models.

Similar constructions can be made for general gauge theories with a compact Lie group G and a connection form.

Over a manifold however, assumptions like diffeomorphism invariance are needed to make the duality exact (smearing Wilson loops is tricky).

Michael A. Levin and Xiao-Gang Wen have also defined string-nets using tensor categories that are objects very similar to spin networks.

In mathematics, spin networks have been used to study skein modules and character varieties, which correspond to spaces of connections.