A Jordan-Wigner transformation for the $t-J$ and Hubbard models with holes

A Jordan-Wigner (JW) transformation for the $t-J$ and Hubbard models is described. Introduced are holon and doublon particles for hole and double occupied sites. There is only a single spin sector particle. Flux tubes occur in a naturel fashion, within a specific gauge, when the method is adapted to two dimensions. In order to accommodate three dimensions ``flux sheets’’ are defined. The adaptation of the method to the $t-J$-model in the context of high $T_c$ is described.