On symmetry properties of states of quantum many-particle systems

Abstract:
We consider the origin of the microscopic description of correlations in quantum many-particle systems, obeying various symmetry properties, namely Bose-Einstein, Fermi-Dirac and fractional statistics. For correlation operators that give the alternative description of the quantum state evolution of many-particle systems, we deduce the von Neumann hierarchy of nonlinear equations and the BBGKY hierarchy.