On the discrete spectrum of the Hamiltonians of n-particle systems with n → ∞ in function spaces with various permutation symmetries

The restrictions of the nonrelativistic energy operators Hn of the relative motion of a system of n identical particles with short-range interaction potentials to subspaces M of functions with various permutation symmetries are considered. It is proved that, for each of these restrictions, there exists an infinite increasing sequence of numbers Nj, j = 1, 2, …, such that the discrete spectrum of each operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{N_j }$$\end{document} on M is nonempty. The family {M} of considered subspaces is, apparently, close to maximal among those which can be handled by the existing methods of study.