The Idea
Spin networks provide a language to describe quantum geometry of space. Spin foam does the same job on spacetime. A spin network is a one-dimensional graph, together with labels on its vertices and edges which encodes aspects of a spatial geometry.
Spacetime is considered as a superposition of spin foams, which is a generalized Feynman diagram where instead of a graph we use a higher-dimensional complex. In topology this sort of space is called a 2-complex. A spin foam is a particular type of 2-complex, together with labels for vertices, edges and faces. The boundary of a spin foam is a spin network, just as in the theory of manifolds, where the boundary of an n-manifold is an (n-1)-manifold.
In Loop Quantum Gravity, the present Spinfoam Theory has been inspired by the work of Ponzano-Regge Model. The idea was introduced in and later developed into the Barret-Crane Model. The formulation that is used nowadays is commonly called EPRL by the name of the authors of a series of seminal papers, but the theory has seen also fundamental contributions coming from the work of many persons such as Laurent Freidel (FK model) and Jerzy Lewandowski (KKL model).
Read more about this topic: Spin Foam
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