Barrett–Crane model

-valued 2-form, i.e. taking values in the Lie algebra of a special orthogonal group.

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 action, but its path integral amplitude corresponds to the degenerate

However, if analysed with the tools of loop quantum gravity the Barrett–Crane model gives an incorrect long-distance limit [1], and so the model is not identical to loop quantum gravity.