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In physics, a spin foam is a four-dimensional graph made out of two-dimensional faces that represents one of the configurations that must be summed to obtain Feynman's path integral (functional integration) describing the alternative formulation of quantum gravity known as loop gravity or loop quantum gravity.

Spin foam in loop quantum gravity

In loop quantum gravity there are some results from a possible canonical quantization of general relativity at the Planck scale. Any path integral formulation of the theory can be written in the form of a spin foam model, such as the Barrett-Crane model. A spin network is defined as a diagram (like Feynman diagram) which make 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.

The idea

Spin networks provide a language to describe quantum geometry of space and spin foam does the same job on spacetime. Spin foam and spin networks can be thought of as one of the categories:

• abstract,
• embedded in a smooth, analytical piecewise-linear manifold,
• fixed triangulated.

Spacetime is considered as a quantic 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-dimensional complex. It specifes a class of complexes and labels for vertices, edges, faces, etc..

See also

• Loop quantum gravity
• Invariance mechanics

References

Spin foam on arxiv.org

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