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. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation often simplifies calculation because simple diagrams may be used to represent complicated functions. Roger Penrose is credited with the invention of spin networks in 1971, although similar diagrammatic techniques existed before that time.

Spin networks have been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin and others. They can also be used to construct a particular functional on the space of connections which is invariant under local gauge transformations.