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Theory of Supersolidity

After reviewing some experimental facts, and early theories, I sketch the Hartree-Fock description of Boson solids, emphasizing the contrast with the Fermion case in that the natural solution is a product of local wave-functions. I then investigate the Boson Hubbard model to demonstrate that the local functions are not orthogonal and exemplify a novel state of matter which has superflow but not ODLRO, below a cooperative thermal transition. I then discuss whether or not these ideas actually apply to solid He.