Dirac equation for embedded 4-geometries
  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. 
Maciej Trzetrzelewski
hep-th gr-qc