Barrett-Crane model
From Wikipedia, the free encyclopedia
This article does not cite any references or sources. (February 2007) Please help improve this article by adding citations to reliable sources. Unverifiable material may be challenged and removed. |
The Barrett-Crane model is a model in loop quantum gravity which was defined using the Plebanski action.
The B field in the action is supposed to be a so(3,1)-valued 2-form, i.e. taking values in the Lie algebra of a special orthogonal group. The term
in the action has the same symmetries as it does to provide the Einstein-Hilbert action. But the form of
- Bij
is not unique and can be posed by the different forms:
where ei field is tetrads and εijkl is antisymmetric symbol of the so(3,1)-valued 2-form fields.
The Plebanski action can be constrained to produce the BF model which is a theory of no local degrees of freedom. John W. Barrett and Louis Crane modeled the analogous constraint on the summation over spin foam.
The Barrett-Crane model on spin foam quantizes the Plebanski theory, but its path integral amplitude corresponds to the degenerate B field and not the specific definition
- ,
which formally satisfies the Einstein's field equation of general relativity. However, the Barrett-Crane vertex is known to give an incorrect long-distance limit [1] and cannot be used a model of physics.