The Barrett–Crane model is a model in quantum gravity

Quantum gravity

Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

 which was defined using the Plebanski action

Plebanski action

General relativity and supergravity in all dimensions meet each other at a common assumption:Using these assumptions one can construct an effective field theory in low energies for both...

.

The field in the action is supposed to be a -valued 2-form, i.e. taking values in the Lie algebra

Lie algebra

In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...

 of a special orthogonal group. The term


in the action has the same symmetries as it does to provide the Einstein-Hilbert action

Einstein-Hilbert action

The Einstein–Hilbert action in general relativity is the action that yields the Einstein's field equations through the principle of least action...

. But the form of


is not unique and can be posed by the different forms:

• 
• 

where field is tetrad

Tetrad

Tetrad may refer to:* Tetrad , Bivalents or Tetrad of homologous chromosomes consisting of four synapsed chromatids that become visible during the Pachytene stage of meiotic prophase...

s and is antisymmetric symbol of the -valued 2-form fields.

The Plebanski action can be constrained to produce the BF model

BF model

The BF model is a topological field theory, which when quantized, becomes a topological quantum field theory. BF stands for background field...

 which is a theory of no local degrees of freedom

Degrees of freedom (physics and chemistry)

A degree of freedom is an independent physical parameter, often called a dimension, in the formal description of the state of a physical system...

. John W. Barrett

John W. Barrett

John W. Barrett is professor of mathematical physics at the University of Nottingham. He is a quantum gravity researcher who is well-known for the Barrett-Crane model of quantum gravity.-Not to be confused with:...

 and Louis Crane modeled the analogous constraint on the summation over spin foam

Spin foam

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 description of quantum gravity...

.

The Barrett–Crane model on spin foam quantizes the Plebanski action

Plebanski action

General relativity and supergravity in all dimensions meet each other at a common assumption:Using these assumptions one can construct an effective field theory in low energies for both...

, but its path integral

Functional integration

Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions...

 amplitude corresponds to the degenerate field and not the specific definition
,

which formally satisfies the Einstein's field equation of general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. However, if analysed with the tools of loop quantum gravity

Loop quantum gravity

Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

the Barrett–Crane model gives an incorrect long-distance limit http://arxiv.org/abs/0708.0883, and so the model is not identical to loop quantum gravity.