Commuting Simplicity and Closure Constraints for 4D Spin Foam Models

Understand

Spin Foam Models are supposed to be discretised path integrals for quantum gravity constructed from the Plebanski-Holst action.

• The reason for there being several models currently under consideration is that no consensus has been reached for how to implement the simplicity constraints.
• Indeed, none of these models strictly follows from the original path integral with commuting B fields, rather, by some non standard manipulations one always ends up with non commuting B fields and the simplicity constraints become in fact anomalous which is the source for there being several inequivalent strategies to circumvent the associated problems.
• In this article, we construct a new Euclidian Spin Foam Model which is constructed by standard methods from the Plebanski-Holst path integral with commuting B fields discretised on a 4D simplicial complex.