Spin Foam Article Index for
Spin
Website Links For
Spin
 

Information About

Spin Foam





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 Network s provide a representation for computations of amplitudes between two different Hypersurface s of the Manifold . Any evolution of Spin Network provides a spin foam over a Manifold of one dimensional higher than the dimensions of the corresponding spin network. A spin foam may be viewed as a Quantum History .


THE IDEA

Spin Network s 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 complecies. 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..