Remarks on mathematical structure of BRST theories

A number of rigorous results concerning the mathematical structure of quantum systems with the BRST symmetry are presented. For studying model-independent properties of such systems, a generalization of the Strocchi-Wightman theory is suggested, which is a Wightman type theory in the Krein space with an OpJ*-algebra of physical and ghost fields. It is proved that the BRST charge operatorQ is either bounded with (Q)={0} or unbounded with (Q)=¢. A number of conditions equivalent to the no-ghost theorem (which states that the kernel ofQ is non-negative) are derived.