Initial-value problem for the Bogolyubov hierarchy for quantum systems of particles - Gerasimenko, V. I.; Shtyk, V. O. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We construct cumulant (semi-invariant) representations for a solution of the initial-value problem for the Bogolyubov hierarchy for quantum systems of particles. In the space of sequences of trace-class operators, we prove a theorem on the existence and uniqueness of a solution. We study the equivalence problem for various representations of a solution in the case of the Maxwell-Boltzmann statistics.