Functional Integrals for Hubbard Operators and Projection Methods for Strong Interaction

We discuss problems of functional integral formalisms in a constrained fermionic Fock space. A functional integral is set up for the Hubbard model using generalized coherent states which lie either in the constrained or in the full Fock space. The projection for the latter states is implemented through a reduction of the charge fluctuations which induce transitions between the constrained and full space. The Lagrangian is expressed in terms of two complex fields representing spin and charge excitations, and one Grassmann field signifying hole excitations. Here, the charge excitations denote transitions between states with empty and doubly occupied sites. The projection method is inspired by the observation that the local interaction in the model resembles a magnetic field in the space of charge fluctuations. Hence the projection is understood as an infinite magnetic field in a spin path integral.