Dirac equation for embedded 4-geometries

TL;DR

This paper develops a Dirac-like equation for embedded 4-geometries using Dirac's square root approach, analyzing its implications for quantum singularities in cosmological models.

Contribution

It introduces a novel Dirac equation framework for embedded 4-geometries, extending quantum gravity methods to cosmological settings.

Findings

Analysis of Dirac-like equation for Friedmann-Robertson-Walker metrics

Insights into quantum singularity formation

Application of Dirac's square root idea to gravitational constraints

Abstract

We apply Dirac's square root idea to constraints for embedded 4-geometries swept by a 3-dimensional membrane. The resulting Dirac-like equation is then analyzed for general coordinates as well as for the case of a Friedmann-Robertson-Walker metric for spatially closed geometries. The problem of the singularity formation at quantum level is addressed.