The sp(3) BRST Hamiltonian formalism for the yang-mills fields

The paper presents in all its nontrivial details the sp(3) BRST Hamiltonian formalism. It is based on structuring the extended phase space on many levels. In this picture, the standard BRST symmetry appears as being only the first approximation of a generalized symmetry, acting as a horizontal (same level) operator. The gauge-fixing problem is completely solved by formulating a theorem and a general rule which allow the choice of a simple gauge term. As an example, the Hamiltonian sp(3) quantization of the Yang-Mills model is exhaustively presented.