  In this paper, the possibility to construct a path integral formalism by
using the Hubbard operators as field dynamical variables is investigated. By
means of arguments coming from the Faddeev-Jackiw symplectic Lagrangian
formalism as well as from the Hamiltonian Dirac method, it can be shown that it
is not possible to define a classical dynamics consistent with the full algebra
of the Hubbard $X$-operators. Moreover, from the Faddeev-Jackiw symplectic
algorithm, and in order to satisfy the Hubbard $X$-operators commutation rules,
it is possible to determine the number of constraint that must be included in a
classical dynamical model. Following this approach it remains clear how the
constraint conditions that must be introduced in the classical Lagrangian
formulation, are weaker than the constraint conditions imposed by the full
Hubbard operators algebra. The consequence of this fact is analyzed in the
context of the path integral formalism. Finally, in the framework of the
perturbative theory, the diagrammatic and the Feynman rules of the model are
discussed.
