Abstract
We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as periodic BCs. The symmetry of the system can lead to interesting properties. For instance, the density of a periodic Bose system is an exact constant: ρ(r) = const. Moreover, in the case of perfect spherical symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main result of the article is that symmetry properties and general quantum-mechanical theorems admit equally both crystalline and liquid ground state for a Bose system of any density.
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