Marcinkiewicz's theorem and approximation schemes for many-particle correlation functions: comment on a paper by Rajagopal and Sudarshan

Recently Rajagopal and Sudarshan proposed a generalization of Marcinkiewicz's theorem to quantum systems. From it they conclude that approximation schemes, such that the irreducible equal-time correlation functions vanish for all orders larger than l but are nonvanishing for some l larger than 2, are inconsistent with basic positivity conditions on the density operator. We show that this statement is false for fermion systems. For boson systems the statement is correct and its extension to irreducible correlation functions for unequal times can be made plausible, a fully rigorous proof does not yet seem available, however. The possibility is briefly discussed that an extension of Marcinkiewicz's theorem may hold for fermion systems, provided one confines his attention to equilibrium states of sucyh systems