On p-adic and adelic wave function of the universe

In the Hartle-Hawking approach the wave function for the ground state of a spatially closed universe obtains by Feynman's path integral method. It corresponds to an amplitude of transition from ''nothing'' to 3-dimensional hypersurface over all compact 4-metrics connecting these two 3-space states. This article represents further development of one of the authors' (B.D.) idea that integration over compact real metrics has to be extrapolated to all p-adic compact metrics. Adelic wave function of the Universe, unifies the wave functions calculated over real and p-adic metrics, and yields the space-time discreteness.