Phase representations of the density matrix and quantum distribution functions

A broad class of representations for the density matrix of phase-space functions is proposed. It is shown that all the known quantum distribution functions are particular cases of this representation. The corresponding equations are found. An examination is made of the conditions under which the phase representation may be a quantum distribution function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, Vol. 12, No. 4, pp. 111–115, April, 1969.The author thanks Professor Ya. P. Terletskii for valuable advice.