Spin Foam - The Idea

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).