Editing Spin network (section)

{{Short description|Diagram used to represent quantum field theory calculations}}
{{More citations needed|date=June 2022}}

[[File:Spin-network-after-penrose.svg|thumb|Spin network diagram, after Penrose]]
In [[physics]], a '''spin network''' is a type of diagram which can be used to represent [[Quantum state|states]] and interactions between [[Particle physics|particles]] and [[Quantum field theory|fields]] in [[quantum mechanics]]. From a [[mathematical]] perspective, the diagrams are a concise way to represent [[multilinear function]]s and functions between [[representation theory|representations]] of [[matrix group]]s. The diagrammatic notation can thus greatly simplify calculations.

[[Roger Penrose]] described spin networks in 1971.<ref name=Penrose71/> 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 (mathematics)|functional]] on the space of [[connection (mathematics)|connections]] which is invariant under local [[gauge transformation]]s.