Dynamics of loop quantum gravity and spin foam models in three dimensions

TL;DR

This paper rigorously connects loop quantum gravity and spin foam models in 2+1 dimensions, offering insights that could inform the understanding of dynamics in the more complex 3+1 case.

Contribution

It provides a rigorous regularization of Rovelli's projection operator and clarifies the relationship between loop quantum gravity and spin foam models in three dimensions.

Findings

Established a rigorous connection between loop quantum gravity and spin foam models in 2+1 dimensions.

Provided a new perspective on tackling dynamics in 3+1 dimensions.

Regularized Rovelli's generalized projection operator in canonical 2+1 gravity.

Abstract

We present a rigorous regularization of Rovellis's generalized projection operator in canonical 2+1 gravity. This work establishes a clear-cut connection between loop quantum gravity and the spin foam approach in this simplified setting. The point of view adopted here provides a new perspective to tackle the problem of dynamics in the physically relevant 3+1 case.