Holomorphic Simplicity Constraints for 4d Riemannian Spinfoam Models

TL;DR

This paper introduces a new spinfoam model for 4d Riemannian quantum gravity using holomorphic simplicity constraints, reformulating the theory with spinor variables and Gaussian integrals to enhance the understanding of quantum geometry.

Contribution

It presents a novel spinfoam model based on holomorphic simplicity constraints, utilizing spinor variables and coherent states to reformulate the path integral for quantum gravity.

Findings

Developed a new spinfoam model for 4d Riemannian gravity.

Reformulated the path integral using Gaussian integrals in spinor variables.

Provided a framework connecting classical phase space to quantum geometry.

Abstract

Starting from the reformulation of the classical phase space of Loop Quantum Gravity in terms of spinor variables and spinor networks, we build coherent spin network states and show how to use them to write the spinfoam path integral for topological BF theory in terms of Gaussian integrals in the spinors. Finally, we use this framework to revisit the simplicity constraints reducing topological BF theory to 4d Riemannian gravity. These holomorphic simplicity constraints lead us to a new spinfoam model for quantum gravity whose amplitudes are defined as the evaluation of the coherent spin networks.