A new spinfoam vertex for quantum gravity

TL;DR

This paper introduces a new spinfoam vertex for 4d quantum gravity models that uses a basis of SU(2) coherent states, clarifying geometric interpretation and semiclassical behavior, potentially improving constraint implementation.

Contribution

A novel spinfoam vertex based on SU(2) coherent states that enhances geometric transparency and semiclassical analysis in quantum gravity models.

Findings

Semiclassical states dominate quantum correlations.

Constraints can be expressed directly in new variables.

The basis clarifies geometric interpretation of variables.

Abstract

We introduce a new spinfoam vertex to be used in models of 4d quantum gravity based on SU(2) and SO(4) BF theory plus constraints. It can be seen as the conventional vertex of SU(2) BF theory, the 15j symbol, in a particular basis constructed using SU(2) coherent states. This basis makes the geometric interpretation of the variables transparent: they are the vectors normal to the triangles within each tetrahedron. We study the condition under which these states can be considered semiclassical, and we show that the semiclassical ones dominate the evaluation of quantum correlations. Finally, we describe how the constraints reducing BF to gravity can be directly written in terms of the new variables, and how the semiclassicality of the states might improve understanding the correct way to implement the constraints.