In physics, the topological structure of spinfoam or spin foam[1] consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity.
The resulting path integral represents a sum over all the possible configurations of spin foam.[how?]
A spin network is a two-dimensional graph, together with labels on its vertices and edges which encode aspects of a spatial geometry.
A spin network is defined as a diagram like the Feynman diagram which makes a basis of connections between the elements of a differentiable manifold for the Hilbert spaces defined over them, and for computations of amplitudes between two different hypersurfaces of the manifold.
Spin networks provide a language to describe the quantum geometry of space.
Spacetime can be defined as a superposition of spin foams, which is a generalized Feynman diagram where instead of a graph, a higher-dimensional complex is used.
A spin foam is a particular type of 2-complex, with labels for vertices, edges and faces.
In loop quantum gravity, the present spin foam theory has been inspired by the work of Ponzano–Regge model.
The idea was introduced by Reisenberger and Rovelli in 1997,[2] and later developed into the Barrett–Crane model.
The formulation that is used nowadays is commonly called EPRL after the names of the authors of a series of seminal papers,[3] but the theory has also seen fundamental contributions from the work of many others, such as Laurent Freidel (FK model) and Jerzy Lewandowski (KKL model).
The summary partition function for a spin foam model is