Abstract
The foundation of hermitian Fermi operator which is usually interpreted as Feddeev-Popov ghost is dicussed. Its representation and path-integral formulae for both transition amplitude and Euclidean trace are given. A quantum mechanical model with BRS invariance is also discussed to clarify that in certain types of stochastic differential equations the vanishing of the vacuum energy can be viewed as the consequences of the quartet mechanism in the operator formalism.

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