It is shown that the properties of positive mass and energy, and of causality lead in quantum field theory to problems in the theory of analytic completion. A representation for the double commutator previously proved the most general is stated, and its connection with analytic completion noted. A similar representation for the triple commutator is proved to satisfy causality and the positive mass and energy condition, but is not shown to give all the functions with these properties. A conjecture about the envelopes of holomorphy of domains occurring in the discussion of analytic properties of the four-point Green’s function is made. Integral representations for then-fold multiple commutator are proposed, and for some other combinations of Wightman functions. These representations lead to some results in analytic completion.