A simpler way of imposing simplicity constraints

TL;DR

This paper proposes a simplified method for imposing simplicity constraints in a holomorphic Spin Foam model by applying them directly to the propagator, maintaining the semi-classical limit while easing calculations.

Contribution

It introduces a new approach to impose simplicity constraints directly on the Spin Foam propagator, simplifying computations without losing the semi-classical Regge limit.

Findings

Both approaches have the same leading asymptotic behaviour.

Differences between approaches appear at higher order.

The new method simplifies calculations in Spin Foam models.

Abstract

We investigate a way of imposing simplicity constraints in a holomorphic Spin Foam model that we recently introduced. Rather than imposing the constraints on the boundary spin network, as is usually done, one can impose the constraints directly on the Spin Foam propagator. We find that the two approaches have the same leading asymptotic behaviour, with differences appearing at higher order. This allows us to obtain a model that greatly simplifies calculations, but still has Regge Calculus as its semi-classical limit.