Spinfoam

In physics, a spinfoam or spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed by functional integration to obtain a Feynman's path integral description of quantum gravity. It is closely related to loop quantum gravity.

Loop quantum gravity has a covariant formulation that, at present, provides the best formulation of the dynamics of the theory of quantum gravity. This is a quantum field theory where the invariance under diffeomorphisms of general relativity is implemented. The resulting path integral represents a sum over all the possible configuration of the geometry, coded in the spinfoam.

A spin network is a one-dimensional graph, together with labels on its vertices and edges which encodes aspects of a spatial geometry.

A spin network is defined as a diagram (like the Feynman diagram) that makes a basis of connections between the elements of a differentiable manifold for the Hilbert spaces defined over them. Spin networks provide a representation for computations of amplitudes between two different hypersurfaces of the manifold. Any evolution of spin network provides a spin foam over a manifold of one dimension higher than the dimensions of the corresponding spin network. A spin foam may be viewed as a quantum history.

Spin networks provide a language to describe quantum geometry of space. Spin foam does the same job on spacetime.

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