Dirac equation for embedded 4-geometries

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.

25 pages, 6 figures, v2: extended version, v3: published version, minor corrections

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