On Functional Fourier Transformation for the Hubbard Model and Similar Models

Describing spin ↑ ‐electrons the particle number operators n i ↓ are replaced under the functional integral directly by c ‐numbers v i ↓( t ) using a δ‐functional instead of the Hubbard‐Stratonovich transformation. The Green function of the Hubbard model is thus exactly represented as an averaged Green function of electrons moving in a stochastic potential Uv i ↓( t ). The probability distribution for the stochastic process v ↓ containing the many body aspect and the information about the ↓‐electrons is determined. The v i ↓( t ) are only allowed to jump between 0 and 1 reflecting the property of Fermion particle number operators. This exact scheme can be interpreted as a dynamically generalized alloy analogy.