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We consider the third quantization in quantum cosmology of a minisuperspaceextended by the Eisenhart-Duval lift. We study the third quantization based onboth Klein-Gordon type and Dirac-type equations in the extended minisuperspace.Spontaneous creation of "universes" is investigated upon the quantization of asimple model. We find that the quantization of the Dirac-type wave functionreveals that the number density of universes is expressed by the Fermi-Diracdistribution. We also calculate the entanglement entropy of the multi-universesystem.

Third quantization for scalar and spinor wave functions of the Universe in an extended minisuperspace