Barrett–Crane model
The Barrett–Crane model is a model in quantum gravity, first published in 1998, which was defined using the Plebanski action.[1][2]
The field in the action is supposed to be a -valued
in the action has the same symmetries as it does to provide the Einstein–Hilbert action. But the form of
is not unique and can be posed by the different forms:
where is the
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 field and not the specific definition
- ,
which formally satisfies the
References
- ^
Barrett, John W.; Louis Crane (1998), "Relativistic spin networks and quantum gravity", J. Math. Phys., 39 (6): 3296–3302, doi:10.1063/1.532254
- ^ Barrett, John W.; Louis Crane (2000), "A Lorentzian signature model for quantum general relativity", Classical and Quantum Gravity, 17 (16): 3101–3118,