large $U$ limit (it is the only assumption) with the use of the projection technique we can find in a straightforward way the final form of the Hamiltonian in this limit without using perturbation expansion or canonical transformation. The resulting Hamiltonian, obtained in this way, is very complicated. It, however, explicitly shows all possible magnetic, nonmagnetic or more complex competitive interaction processes very deeply hidden in the original Hamiltonian written in the site representation (1). It is the aim of this paper just to reveal these important but normally invisible elementary interactions. One important advantage might be that a given approach to the unsolvable Hubbard problem can be tested with respect to the types of neglected interaction processes. Besides, the new and straightforward method, presented in this paper, can easily be adopted to clusters of any size and also to another types of model Hamiltonians.

The paper is organized as follows. In Sec. 2 we find the exact solution of the Hubbard dimer (5) and give the exact expressions for the annihilation operators $c_{I,1(2),\sigma }$ in the dimer representation. In Sec. 3 we derive the Hubbard dimer Hamilonian (5) in the large $U$ limit. With the use of the projection 