The projection-like techniques for Wigner's distribution function

Starting from the quantum Liouville equation for many-particle distribution function an evolution equation for fully factorized and symmetrized Wigner's distribution function is derived. Our approach is formally similar to the projection operator method. Details of the used techniques are presented as an example of the two-particle system.A greater part of the presented paper was realized under the auspices of the late Professor A. Pawikowski. The author wants to dedicate this paper to his memory. He would also like to thank Dr. J. uczka for critical reading of the first version of this paper and valuable advice.