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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 can thus greatly simplify calculations.
Roger Penrose described spin networks in 1971.[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.