Dynamical Model and Path Integral Formalism for Hubbard Operators

Abstract

In this paper, the possibility to construct apath integral formalism by using the Hubbard operatorsas field dynamical variables is investigated. By meansof arguments coming from the Faddeev-Jackiw symplectic Lagrangian formalism as well as from theHamiltonian Dirac method, it can be shown that it is notpossible to define a classical dynamics consistent withthe full algebra of the Hubbard X-operators. Moreover, from the Faddeev-Jackiw symplectic algorithm,and in order to satisfy the Hubbard X-operatorscommutation rules, it is possible to determine thenumber of constraints that must be included in aclassical dynamical model. Following this approach, it isclear how the constraint conditions that must beintroduced in the classical Lagrangian formulation areweaker than the constraint conditions imposed by the full Hubbard operators algebra. The consequenceof this fact is analyzed in the context of the pathintegral formalism. Finally, in the framework of theperturbative theory, the diagrammatic and the Feynman rules of the model are discussed.