In the covariant canonical formalism of Yang-Mills theory and of the internal-Lorentz part of vierbein formalism, a new invariance is found under " another BRS transformation" satisfying the nilpotency property. In this transformation, the roles of the Faddeev-Popov ghost c in the BRS transformation are played by the Faddeev-Popov anti-ghost c. Some im-plications of this new symmetry including the Ward-Takahashi identities following from it are discussed.
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Izumi Ojima (1980) studied this question.
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