Abstract
The paper offers the complete form of the BRST charges and of the extended Hamiltonian for the first-rank theories in the context of the sp(3) BRST symmetry. A theorem is proposed in order to solve the problem of existence and uniqueness of a gauge fixed Hamiltonian in this context. As a general result, it is verified that the standard and the sp(2) theories could be recovered as particular cases of our generalized symmetry.
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