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The wave function (or more precisely the wave Functional ) is a functional of the Metric Tensor defined at a (D-1)-dimensional compact surface, the Universe, where D is the Spacetime dimension. The precise form of the Hartle-Hawking state is the path integral over all D-dimensional geometries that have the required Induced Metric on their boundary.

Such a wave function of the Universe can be shown to satisfy the Wheeler-deWitt Equation .


REFERENCES

  • Hawking, Hertog, and Reall, " Brane New World ", ''Phys. Rev.'' D62 (2000) 043501.

  • J. Hartle and S. W. Hawking, "Wave function of the universe", ''Phys. Rev.'' D28, 2960 (1983).