Symmetry in Nonlinear Mathematical Physics - 2009

Denis Polishchuk (Taras Shevchenko National University of Kyiv, Ukraine)

On symmetry properties of states of quantum many-particle systems

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.