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| In ], a '''spin foam''' is a |
In ], a '''spin foam''' is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a ] (]) description of ]. It is closely related to ]. | ||
| ==Spin foam in loop quantum gravity== | ==Spin foam in loop quantum gravity== | ||
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| ==The idea== | ==The idea== | ||
| ]s provide a language to describe ] of space |
]s provide a language to describe ] of space. Spin foam does the same job on spacetime. A spin network is a one-dimensional ], 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 ] where instead of a graph we use a higher-dimensional complex. In ] this sort of space is called a 2-]. A spin foam is a particular type of 2-complex, together with labels for ], edges and ]. The boundary of a spin foam is spin network, just as in the theory of ], where the boundary of an n-manifold is an (n-1)-manifold. | ||
| * abstract, | |||
| * embedded in a smooth, analytical piecewise-linear manifold, | |||
| * fixed triangulated. | |||
| ⚫ | Spacetime is considered as a |
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| ==See also== | ==See also== | ||
Revision as of 07:06, 20 August 2008
In physics, a spin foam is a topological structure made out of two-dimensional faces that represents one of the configurations that must be summed to obtain a Feynman's path integral (functional integration) description of quantum gravity. It is closely related to 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. 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 spin network, just as in the theory of manifolds, where the boundary of an n-manifold is an (n-1)-manifold.
See also
References
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