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Abstract
This review is concerned with the concept that in a many-body system of bosons or fermions, it is possible to have an off-diagonai long-range order of the reduced density matrices in the coordinate space representation. The onset of such an order ieads to a new thermodynamic phase of the system. It is reasonabie to assume that superfluid He II and the superconductors are phases characterized by the existence of such an order. (W.D.M.)
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